Answer:
$301.23
Step-by-step explanation:
We have that the function of wealth is U (w) = w ^ (1/2)
So, since what you have at the start is 100, we replace:
U (w) = 100 ^ (1/2)
U = 10
Now we have two cases:
the first one we win, then the winnings would be 100 minus the cost of the lottery, that is 36 and to that add G of the prize:
100 - 36 + G = 64 + G
In the second case, where we lose, the subtraction of 100 that we have minus the cost of the lottery would be equal 36
100 - 36 = 64
Therefore, we have to win with an 18% probability, therefore losing would be 82% (100% - 18%)
0.18 * (64 + G) ^ (1/2) + 0.82 * 64 ^ (1/2)
solving:
0.18 * (64 + G) ^ (1/2) + 6.56
Now this is equal to U which is equal to 10:
10 = 0.18 * (64 + G) ^ (1/2) + 6.56
(10 - 6.56) /0.18 = (64 + G) ^ (1/2)
(64 + G) ^ (1/2) = 19.11
(64 + G) = 365.23
G = 365.23 - 64
G = 301.23
Therefore, the smallest G prize size that the lottery will be willing to buy is $ 301.23
A mattress store sells only king, queen and twin-size mattresses. Sales records at the store indicate that the number of queen-size mattresses sold is one-fourth the number of king and twin-size mattresses combined. Records also indicate that three times as many king-size mattresses are sold as twin-size mattresses. Calculate the probability that the next mattress sold is either king or queen-size.
Answer:
The probability that the next mattress sold is either king or queen-size is P=0.8.
Step-by-step explanation:
We have 3 types of matress: queen size (Q), king size (K) and twin size (T).
We will treat the probability as the proportion (or relative frequency) of sales of each type of matress.
We know that the number of queen-size mattresses sold is one-fourth the number of king and twin-size mattresses combined. This can be expressed as:
[tex]P_Q=\dfrac{P_K+P_T}{4}\\\\\\4P_Q-P_K-P_T=0[/tex]
We also know that three times as many king-size mattresses are sold as twin-size mattresses. We can express that as:
[tex]P_K=3P_T\\\\P_K-3P_T=0[/tex]
Finally, we know that the sum of probablities has to be 1, or 100%.
[tex]P_Q+P_K+P_T=1[/tex]
We can solve this by sustitution:
[tex]P_K=3P_T\\\\4P_Q=P_K+P_T=3P_T+P_T=4P_T\\\\P_Q=P_T\\\\\\P_Q+P_K+P_T=1\\\\P_T+3P_T+P_T=1\\\\5P_T=1\\\\P_T=0.2\\\\\\P_Q=P_T=0.2\\\\P_K=3P_T=3\cdot0.2=0.6[/tex]
Now we know the probabilities of each of the matress types.
The probability that the next matress sold is either king or queen-size is:
[tex]P_K+P_Q=0.6+0.2=0.8[/tex]
in four lines determine how to find a perimeter and area of garden with specific dimensions
Answer:
[tex]Perimeter\ of\ the\ Garden\ =2(l1*b1)[/tex]
[tex]Area\ of\ the\ garden\ =l1*b1[/tex]
Step-by-step explanation:
Let assume the l1 is the length of the garden and b1 is the breadth of garden then
[tex]Perimeter\ of\ the\ Garden\ = 2 ( L ength + Breadth )\\Perimeter\ of\ the\ Garden\ =2(l1*b1)[/tex]
Now,
[tex]Area\ of\ Garden\ = Length * Breadth[/tex]
[tex]Area\ of\ the\ garden\ =l1*b1[/tex]
A study seeks to answer the question, "Does Vitamin C level in the breast milk of new mothers reduce the risk of allergies in their breastfed infants?" The study concluded that high levels of vitamin C (measured in mg) were associated with a 30 percent lower risk of allergies in the infants. In this scenario, "levels of vitamin C (measured in milligrams)" is what type of variable?
Answer:
Quantitative variable
Step-by-step explanation:
The objective in this study is to find the of variable used to conduct the study. The type of variable used to conduct this study is Qualitative variable.
There are majorly two types of variable. These are:
Categorical VariableQuantitative variableCategorical variables are types of variables that are grouped based on some similar characteristics. The nominal scale and the ordinal scale falls under this group of variable.
The nominal scale is an act of giving name to a particular object or concept in order to identify or classify that particular thing.
On the other hand, The ordinal scale possess all the characteristics of nominal scale but here the variables can be ordered. It can be used to determine whether the item is greater or less. It express the indication of order and magnitude.
In Qualitative variables; variables are measured on a numeric scale. From the given question , This type of variable is used to measure the high levels of vitamin C (measured in mg) which were associated with a 30 percent lower risk of allergies in the infants.
The levels of vitamin C could range from 0 mg to certain mg therefore we can measure vitamin C in numerical values of measurement (Quantitative variable).
If 4000 hours= 240,000 minutes and you make a 10 minute video, how many people will need to view the video to get 4000 hours of view time?
Answer:
24000
Step-by-step explanation:
because 24000 * 10 =240000
1. O perímetro de um quadrado é 20 cm. Determine sua diagonal. 1 ponto a) 2 √5 cm b) 20√2 cm c) 5√2 cm d) 2√10 cm
Answer:
c) 5√2 cm
Step-by-step explanation:
A square with side length l has a perimeter given by the following equation:
P = 4l.
In this question:
P = 20
So the side length is:
4l = 20
l = 20/4
l = 5
Diagonal
The diagonal forms a right triangle with two sides, in which the diagonal is the hypothenuse. Applying the pytagoras theorem.
[tex]d^{2} = l^{2} + l^{2}[/tex]
[tex]d^{2} = 5^{2} + 5^{2}[/tex]
[tex]d^{2} = 50[/tex]
[tex]d = \pm \sqrt{50}[/tex]
Lenght is a positive meausre, so
[tex]d = \sqrt{50}[/tex]
[tex]d = \sqrt{2 \times 25}[/tex]
[tex]d = \sqrt{2} \times \sqrt{25}[/tex]
[tex]d = 5\sqrt{2}[/tex]
So the correct answer is:
c) 5√2 cm
What is the result of adding these two equations? 2x+3y=-5 5x-y=-12
Answer:
[tex]x = \frac{-41}{17} , y = \frac{-1}{17}[/tex]
Step-by-step explanation:
Step(i):-
Given equations are 2 x+3 y=-5 ...(i)
5 x-y=-12 ...(ii)
Multiply equation (ii) by '3'
2 x + 3 y = -5
15 x - 3 y = - 36
17 x = - 41
[tex]x = \frac{-41}{17}[/tex]
Step(ii):-
Substitute [tex]x = \frac{-41}{17}[/tex] in equation (i)
2 ([tex]\frac{-41}{17}[/tex]+3 y=-5
3 y = - 5 + [tex]\frac{82}{17}[/tex]
[tex]3 y = \frac{-85 + 82}{17} = \frac{-3}{17}[/tex]
[tex]y = \frac{-1}{17}[/tex]
The solution of the two equations
( x, y ) = [tex](\frac{-41}{17} , \frac{-1}{17})[/tex]
A computer manufacturer conducted a survey. It showed that a younger customer will not necessarily purchase a lower or higher priced computer. What is likely true? There is no correlation between age and purchase price. There is a correlation between age and purchase price. There may or may not be causation. Further studies would have to be done to determine this. There is a correlation between age and purchase price. There is probably also causation. This is because there is likely a decrease in the purchase price with a decrease in age.
Answer:
There is no correlation between age and purchase price
Step-by-step explanation:
In the survey, the researcher found out that a younger customer will not necessarily purchase a lower or higher priced computer thing it is likely true that there might be no correlation between purchase price and age.
It assumes that a younger customer can buy either buy a lower priced computer or can also buy a higher priced if he or she has the money for it.
Find the percent of area under a normal curve between the mean and the given number of standard deviations from the mean. (Note that positive indicates above the mean, while negative indicates below the mean.)0.20
Answer:
15.86%
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Percent of area between the mean and 0.20 standard deviations from the mean:
pvalue of Z = 0.2 subtracted by the pvalue of Z = -0.2
Z = 0.2 has a pvalue of 0.5793
Z = -0.2 has a pvalue of 0.4207
0.5793 - 0.4207 = 0.1586
So this percentage is 15.86%
Which expressions are equivalent to 64^1Check all that apply
The right answers are:
4^38^22^6Hope it helps.
please see the attached picture for full solution
Good luck on your assignment
What’s the correct answer for this question?
Answer:
C.
Step-by-step explanation:
First finding height using Pythagoras theorem
(H)²=(B)²+(P)²
8.2²=5.4²+P²
P² = 67.24 - 29.16
P² = 38.08
P = 6.2
Now
Volume of cone = (1/3)πr²h
= (1/3)(3.14)(5.4)²(6.2)
= (1/3)(567.9)
= 189.2 cm³
A newborn baby whose Apgar score is over 6 is classified as normal and this happens in 80% of births. As a quality control check, an auditor examined the records of 100 births. He would be suspicious if the number of normal births in the sample of 100 births fell below the lower limit of "usual." What is that lower limit?
Answer:
The lower limit is 72.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
If X is more than 2 standard deviations from the mean, it is unusual.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question, we have that:
[tex]n = 100, p = 0.8[/tex]
So
[tex]\mu = 0.8, s = \sqrt{\frac{0.8*0.2}{100}} = 0.04[/tex]
He would be suspicious if the number of normal births in the sample of 100 births fell below the lower limit of "usual." What is that lower limit?
2 standard deviations below the mean is the lower limit, so X when Z = -2.
Proportion:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-2 = \frac{X - 0.8}{0.04}[/tex]
[tex]X - 0.8 = -2*0.04[/tex]
[tex]X = 0.72[/tex]
Out of 100:
0.72*100 = 72
The lower limit is 72.
2x2 + 3x ANSWER TO THIS
Answer:
x(2x+3)
Step-by-step explanation:
Im guessing 2x2 is 2x^2
2x^2 + 3x = 0
x(2x+3)
Simplify.
(8^3)7 = 8n
Answer:
448I think
Step-by-step explanation:
Answer:21
Step-by-step explanation:
A random sample of 1,000 StatCrunchU students contains 598 female and 402 males. We analyze responses to the question, "What is the total amount (in dollars) of your student loans to date?" Two sample T confidence interval: μ 1: Mean of Loans where Gender="Female" μ 2: Mean of Loans where Gender="Male" μ 1 − μ 2: Difference between two means (without pooled variances) 95% confidence interval results: Difference Sample Diff. Std. Err. DF L. Limit U. Limit μ 1 − μ 2 516.74334 368.41116 907.34739 -206.29374 1239.7804 What can we conclude from the 95% confidence interval? Check all that apply. Group of answer choices
Based on the information given, these are the conclusions we can draw from the 95% confidence interval.
Here, we have,
From the provided 95% confidence interval, we can make the following conclusions:
The point estimate of the difference between the mean student loans for females and males is 516.74334 dollars.
The standard error of the difference between the means is 368.41116 dollars.
The degrees of freedom (DF) associated with the confidence interval is 907.34739.
The lower limit of the confidence interval is -206.29374 dollars.
The upper limit of the confidence interval is 1239.7804 dollars.
The confidence interval does not contain zero.
Since zero is not within the interval, we can conclude that the difference between the mean student loans for females and males is statistically significant at the 95% confidence level.
Based on the information given, these are the conclusions we can draw from the 95% confidence interval.
Learn more about confidence interval here:
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The estimated difference in the mean student loans between females and males is 516.74334.
There is a 95% confidence that the true difference in means falls within the range of -206.29374 to 1239.7804.
Based on the 95% confidence interval provided for the difference in means between the loans of female and male StatCrunchU students, we can draw the following conclusions:
The sample difference in means is 516.74334.
The standard error of the difference is 368.41116.
The degrees of freedom (DF) for the analysis is 907.34739.
The lower limit of the confidence interval is -206.29374.
The upper limit of the confidence interval is 1239.7804.
Therefore, we can conclude the following:
The estimated difference in the mean student loans between females and males is 516.74334.
There is a 95% confidence that the true difference in means falls within the range of -206.29374 to 1239.7804.
Note: Since the confidence interval includes both positive and negative values, we cannot conclude with certainty whether there is a significant difference or not in the mean student loans between females and males. The confidence interval suggests that the difference could be positive, negative, or even zero.
For more such questions on difference in the mean
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What is the simplified value of the exponential expression 27 1/3?
1/3
1/9
3
9
Answer:3
Step-by-step explanation:
Answer:
C.3
Step-by-step explanation:
Solve the equation and state a reason for each step.
23+11a-2c=12-2c
Simplifying
23 + 11a + -2c = 12 + -2c
Add '2c' to each side of the equation.
23 + 11a + -2c + 2c = 12 + -2c + 2c
Combine like terms: -2c + 2c = 0
23 + 11a + 0 = 12 + -2c + 2c
23 + 11a = 12 + -2c + 2c
Combine like terms: -2c + 2c = 0
23 + 11a = 12 + 0
23 + 11a = 12
Solving
23 + 11a = 12
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-23' to each side of the equation.
23 + -23 + 11a = 12 + -23
Combine like terms: 23 + -23 = 0
0 + 11a = 12 + -23
11a = 12 + -23
Combine like terms: 12 + -23 = -11
11a = -11
Divide each side by '11'.
a = -1
Simplifying
a = -1
Q‒4. Suppose A is the set composed of all ordered pairs of positive integers. Let R be the relation defined on A where (a,b)R(c,d) means that a+d=b+c.
Prove that R is an equivalence relation.
Find [(2,4)].
Answer:
Step-by-step explanation:
REcall that given a set A, * is a equivalence relation over A if
- for a in A, then a*a.
- for a,b in A. If a*b, then b*a.
- for a,b,c in A. If a*b and b*c then a*c.
Consider A the set of all ordered pairs of positive integers.
- Let (a,b) in A. Then a+b = a+b. So, by definition (a,b)R(a,b).
- Let (a,b), (c,d) in A and suppose that (a,b)R(c,d) . Then, by definition a+d = b+c. Since the + is commutative over the integers, this implies that d+a = c+b. Then (c,d)R(a,b).
- Let (a,b),(c,d), (e,f) in A and suppose that (a,b)R(c,d) and (c,d)R(e,f). Then
a+d = b+c, c+f = d+e. We have that f = d+e-c. So a+f = a+d+e-c. From the first equation we find that a+d-c = b. Then a+f = b+e. So, by definition (a,b)R(e,f).
So R is an equivalence relation.
[(a,b)] is the equivalence class of (a,b). This is by definition, finding all the elements of A that are equivalente to (a,b).
Let us find all the possible elements of A that are equivalent to (2,4). Let (a,b)R(2,4) Then a+4 = b+2. This implies that a+2 = b. So all the elements of the form (a,a+2) are part of this class.
2 Points
Which is a kingdom?
O A. Prokarya
B. Protista
C. Mammalia
O D. Chordata
Answer:
Protista
Step-by-step explanation:
Archaebacteria.
Eubacteria.
Protista.
Fungi.
Plantae.
Animalia.
These are the 6 kingdoms
What is the probability that a senior Physics major and then a sophomore Physics major are chosen at random? Express your answer as a fraction or a decimal number rounded to four decimal places
Answer:
The probability that a senior Physics major and then a sophomore Physics major are chosen at random is 0.0095.
Step-by-step explanation:
The complete question is:
There are 103 students in a physics class. The instructor must choose two students at random.
Students in a Physics Class
Academic Year Physics majors Non-Physics majors
Freshmen 17 15
Sophomores 20 14
Juniors 11 17
Seniors 5 4
What is the probability that a senior Physics major and then a sophomore Physics major are chosen at random? Express your answer as a fraction or a decimal number rounded to four decimal places.
Solution:
There are a total of N = 103 students present in a Physics class.
Some of the students are Physics Major and some are not.
The instructor has to select two students at random.
The instructor first selects a senior Physics major and then a sophomore Physics major.
Compute the probability of selecting a senior Physics major student as follows:
[tex]P(\text{Senior Physics Major})=\frac{n(\text{Senior Physics Major}) }{N}[/tex]
[tex]=\frac{5}{103}\\\\=0.04854369\\\\\approx 0.0485[/tex]
Now he two students are selected without replacement.
So, after selecting a senior Physics major student there are 102 students remaining in the class.
Compute the probability of selecting a sophomore Physics major student as follows:
[tex]P(\text{Sophomore Physics Major})=\frac{n(\text{Sophomore Physics Major}) }{N}[/tex]
[tex]=\frac{20}{102}\\\\=0.1960784314\\\\\approx 0.1961[/tex]
Compute the probability that a senior Physics major and then a sophomore Physics major are chosen at random as follows:
[tex]P(\text{Senior}\cap \text{Sophomore})=P(\text{Senior})\times P(\text{Sophomore})[/tex]
[tex]=0.0485\times 0.1961\\\\=0.00951085\\\\\approx 0.0095[/tex]
Thus, the probability that a senior Physics major and then a sophomore Physics major are chosen at random is 0.0095.
What is the purchase price of the land
Answer:
Answer:B. $100,000
Step-by-step explanation:
x is the number of years since the purchase of the land.
That means that when 0 years have passed by, it is when the land was purchased.
At x = 0, the price of the land was $100,000.
That means that the purchase price of the land is $100,000.
A study of consumer smoking habits includes A people in the 18-22 age bracket (B of whom smoke), C people in the 23-30 age bracket (D of whom smoke), and E people in the 31-40 age bracket (F of whom smoke). If one person is randomly selected from this sample, find the probability of getting someone who is age 23-30 or smokes.
The correct question is:
A study of consumer smoking habits includes 167 people in the 18-22 age bracket (59 of whom smoke), 148 people in the 23-30 age bracket (31 of whom smoke), and 85 people in the 31-40 age bracket (23 of whom smoke). If one person is randomly selected from this sample, find the probability of getting someone who is age 23-30 or smokes
Answer:
The probability of getting someone who is age 23-30 or smokes = 0.575
Step-by-step explanation:
We are given;
Number consumers of age 18 - 22 = 167
Number of consumers of ages 22 - 30 = 148
Number of consumers of ages 31 - 40 = 85
Thus,total number of consumers in the survey = 167 + 148 + 85 = 400
We are also given;
Number consumers of age 18 - 22 who smoke = 59
Number of consumers of ages 22 - 30 who smoke = 31
Number of consumers of ages 31 - 40 who smoke = 23
Total number of people who smoke = 59 + 31 + 23 = 113
Let event A = someone of age 23-30 and event B = someone who smokes. Thus;
P(A) = 148/400
P(B) = 113/400
P(A & B) = 31/400
Now, from addition rule in sets which is given by;
P(A or B) = P (A) + P (B) – P (A and B)
We can now solve the question.
Thus;
P(A or B) = (148/400) + (113/400) - (31/400)
P(A or B) = 230/400 = 0.575
The probability of obtaining a defective 10-year old widget is 66.6%. For our purposes, the random variable will be the number of items that must be tested before finding the first defective 10-year old widget. Thus, this procedure yields a geometric distribution. Use some form of technology like Excel or StatDisk to find the probability distribution. (Report answers accurate to 4 decimal places.) k P(X = k) 1 .666 Correct 2 3 4 5 6 or greater
Answer:
For k = 1:
=NEGBINOMDIST(0, 1, 0.666) = 0.6660
For k = 2:
=NEGBINOMDIST(1, 1, 0.666) = 0.2224
For k = 3:
=NEGBINOMDIST(2, 1, 0.666) = 0.0743
For k = 4:
=NEGBINOMDIST(3, 1, 0.666) = 0.0248
For k = 5:
=NEGBINOMDIST(4, 1, 0.666) = 0.0083
For k = 6:
=NEGBINOMDIST(5, 1, 0.666) = 0.0028
Step-by-step explanation:
The probability of obtaining a defective 10-year old widget is 66.6%
p = 66.6% = 0.666
The probability of obtaining a non-defective 10-year old widget is
q = 1 - 0.666 = 0.334
The random variable will be the number of items that must be tested before finding the first defective 10-year old widget.
The geometric distribution is given by
[tex]$P(X = k) = p \times q^{k - 1}$[/tex]
Solving manually:
For k = 1:
[tex]P(X = 1) = 0.666 \times 0.334^{1 - 1} = 0.666 \times 0.334^{0} = 0.666[/tex]
For k = 2:
[tex]P(X = 2) = 0.666 \times 0.334^{2 - 1} = 0.666 \times 0.334^{1} = 0.2224[/tex]
For k = 3:
[tex]P(X = 3) = 0.666 \times 0.334^{3 - 1} = 0.666 \times 0.334^{2} = 0.0743[/tex]
For k = 4:
[tex]P(X = 4) = 0.666 \times 0.334^{4 - 1} = 0.666 \times 0.334^{3} = 0.0248[/tex]
For k = 5:
[tex]P(X = 5) = 0.666 \times 0.334^{5 - 1} = 0.666 \times 0.334^{4} = 0.0083[/tex]
For k = 6:
[tex]P(X = 6) = 0.666 \times 0.334^{6 - 1} = 0.666 \times 0.334^{5} = 0.0028[/tex]
Using Excel function:
NEGBINOMDIST(number_f, number_s, probability_s)
Where
number_f = k - 1 failures
number_s = no. of successes
probability_s = the probability of success
For the geometric distribution, let number_s = 1
For k = 1:
=NEGBINOMDIST(0, 1, 0.666) = 0.6660
For k = 2:
=NEGBINOMDIST(1, 1, 0.666) = 0.2224
For k = 3:
=NEGBINOMDIST(2, 1, 0.666) = 0.0743
For k = 4:
=NEGBINOMDIST(3, 1, 0.666) = 0.0248
For k = 5:
=NEGBINOMDIST(4, 1, 0.666) = 0.0083
For k = 6:
=NEGBINOMDIST(5, 1, 0.666) = 0.0028
As you can notice solving manually and using Excel yields the same results.
Multiply or divide as indicated x^10/x^4
Answer:
X^6
Step-by-step explanation:
HELP! the function f(x)=200/x+10 models the cost per student of a field trip when x students go on the trip. how is the parent function f(x)=1/x transformed to create the function f(x)=200/x+10
Answer:
stretch of 200 shift up 10 units
Step-by-step explanation:
f(x)=1/x to 200/x+10
Multiply by 200 means a stretch of 200
f(x) = 200/x
Now shift up 10 units
f(x) = 200/x + 10
Answer:
It moves up 10 units
Step-by-step explanation:
f(x) =1/x to 200/x + 10
= 200/x
If we shift up 10 units, we get:
f(x) = 200/x + 10
Hope this helps!
How many tons is 22,000 pounds?
Answer:
1 ton = 2,000 pounds
Step-by-step explanation:
With that said, 22,000 pounds is 11 tons because 2,000 x 11 = 22,000.
So 22,000 pounds is 11 tons.
Hope it helps and pls mark me brainliest if it did! :)
Records on a fleet of trucks reveal that the average life of a set of spark plugs is normally distributed with a mean of 22,100 miles. The fleet owner purchased 18 sets and found that the sample average life was 23,400 miles; the sample standard deviation was 1,412 miles.
a) To decide if the sample data support the company records that the spark plugs average 22,100 miles, state your decision in terms of the null hypothesis. Use a 0.05 level of significance.
b) What is the critical value for the test using a 0.05 level of significance?
c) What is the test statistic?
d) What is your decision?
Answer:
a) We want to conduct a hypothesis in order to see if the true mean is 22100 or not, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 22100[/tex]
Alternative hypothesis:[tex]\mu \neq 22100[/tex]
b) We need to find the degrees of freedom given by:
[tex] df =n-1 = 18-1=17[/tex]
And the critical values for this case are:
[tex] t_{\alpha/2}= 2.110[/tex]
c) [tex]t=\frac{23400-22100}{\frac{1412}{\sqrt{18}}}=3.906[/tex]
d) Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 221100 mi
Step-by-step explanation:
Information provided
[tex]\bar X=23400[/tex] represent the sample mean
[tex]s=1412[/tex] represent the sample standard deviation
[tex]n=18[/tex] sample size
[tex]\mu_o =22100[/tex] represent the value to verify
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value
Part a
We want to conduct a hypothesis in order to see if the true mean is 22100 or not, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 22100[/tex]
Alternative hypothesis:[tex]\mu \neq 22100[/tex]
Part b
We need to find the degrees of freedom given by:
[tex] df =n-1 = 18-1=17[/tex]
And the critical values for this case are:
[tex] t_{\alpha/2}= 2.110[/tex]
Part c
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info we got:
[tex]t=\frac{23400-22100}{\frac{1412}{\sqrt{18}}}=3.906[/tex]
Part d
Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 221100 mi
If f(x) = –8 – 5x, what is f(–4)?
Answer:
12
Step-by-step explanation:
f(-4) = -8-5(-4) = -8+20 = 12
Answer:
f(-4) = 12
Step-by-step explanation:
f(-4) = -8 - 5(-4)
= -8 + 20
= 12
Anyone Can help me? Thanks
Answer:
9.8
Step-by-step explanation:
updated
9^2=x^2+4^2
9*9=x*x+4*4
81=x*x-16
+16. +16
97=x*x
√97=√x*x
√97=x
So the answer is √97, but the question wants it rounded so it's actually 9.8
You are conducting a study to see if the proportion of men over the age of 50 who regularly have their prostate examined is significantly less than 0.3. A random sample of 735 men over the age of 50 found that 203 have their prostate regularly examined. Do the sample data provide convincing evidence to support the claim
Answer:
[tex]z=\frac{0.276 -0.3}{\sqrt{\frac{0.3(1-0.3)}{735}}}=-1.42[/tex]
Now we can claculate the p value with this formula:
[tex]p_v =P(z<-1.42)=0.0778[/tex]
If we use a signifiacn level of 5% we see that the p value is higher than 0.05 so then we have enough evidence to fail to reject the null hypothesis and we can't conclude that the true proportion is significantly higher than 0.3 at 5% of significance.
Step-by-step explanation:
Information to given
n=735 represent the random sample taken
X=203 represent the number of people who have their prostate regularly examined
[tex]\hat p=\frac{203}{735}=0.276[/tex] estimated proportion of people who have their prostate regularly examined
[tex]p_o=0.3[/tex] is the value to verify
z would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to test if the true proportion is less than 0.3, the ystem of hypothesis are.:
Null hypothesis:[tex]p \geq 0.3[/tex]
Alternative hypothesis:[tex]p < 0.3[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info we got:
[tex]z=\frac{0.276 -0.3}{\sqrt{\frac{0.3(1-0.3)}{735}}}=-1.42[/tex]
Now we can claculate the p value with this formula:
[tex]p_v =P(z<-1.42)=0.0778[/tex]
If we use a signifiacn level of 5% we see that the p value is higher than 0.05 so then we have enough evidence to fail to reject the null hypothesis and we can't conclude that the true proportion is significantly higher than 0.3 at 5% of significance.
The length of a rectangle is 4 inches longer than the width. If the area is 390 square inches, find the rectangle's dimensions. Round your answers to the nearest tenth of an inch.
Answer:
17.8 in x 21.8 in
Step-by-step explanation:
Given w=width and l=length
w*l=390
l=w+4, therefore w*(w+4)=390
w^2+4w=390
w^2+4w-390=0
Quadratic equation, solve as such
w=-21.8 or 17.8
Solution can't be negative so w=17.8 in
l=w+4 so l=21.8