Answer:
0.004% probability the student will pass
Step-by-step explanation:
I am going to use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using 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.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]n = 50, p = \frac{1}{4} = 0.25[/tex]
So
[tex]\mu = E(X) = np = 50*0.25 = 12.5[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{50*0.25*0.75} = 3.06[/tex]
If a student guesses on every question, what is the probability the student will pass
Using continuity correction, this is [tex]P(X \geq 25 - 0.5) = P(X \geq 24.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 24.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{24.5 - 12.5}{3.06}[/tex]
[tex]Z = 3.92[/tex]
[tex]Z = 3.92[/tex] has a pvalue of 0.99996
1 - 0.99996 = 0.00004
0.004% probability the student will pass
John conducted a taste test on a new brand of French fries. He gave each participant 5 of the new brand of fries and 5 of the old brand of fries and asked them to rate which brand they preferred. The participants rated both brands of fries as equally preferable. Based on this, he recommended to the manufacturer to move ahead with producing this new brand. However, the brand did not sell well. People reported feeling nauseous after they had consumed a whole portion.
Which validity is weak in this example?
a. internal validity
b. external validity
c. statistical validity
d. construct validity
Answer:
b. external validity
Step-by-step explanation:
External Validity is the applicability of the results of an experiment to the real world. Most times, there are threats to the validity of an experiment which could result in little or no effect on the general population. For example, if the method of selection reflects a measure of bias, then this could affect the result. Also if the participants are taking different aspects of the same test, it could also affect its validity as they may not be able to make a correct conclusion. If the sample size is not reflective of the entire population, it could also pose a threat to the validity of the experiment.
John's experiment is weak in its external validity because it cannot be generalized to the entire population of customers. He has to identify the threats to the validity of his experiment and correct them. For example, the sample selection may be biased.
This table gives a few (x,y) pairs of a line in the coordinate plane. What is the y-intercept of the line?
Answer:
(0,34)
Step-by-step explanation:
I graphed the coordinates of the table on the graph below to find the y-intercept.
Let f(x) = -2x + 7 and g(x) = -6x + 3. Find fg and state its domain.
Answer:
f(g(x))=12x+1
Step-by-step explanation:
f(g(x)) = -2(-6x+3)+7
f(g(x))= 12x-6+7
f(g(x))=12x+1
Domain: All real numbers
please help me on this work please !
solve 5(x+4)<75 sdsdsd
Answer:
x < 11
Step-by-step explanation:
[tex]5(x+4)<75 \\ open \: the \: bracket \: using \: 5 \\ 5x + 20 < 75 \\ subtract \: - 20 \: from \: both \: sides \: [/tex]
[tex]5x + 20 - 20 < 75 - 20 \\ 5x < 55 \\ divide \: both \: sides \: of \: the \: equation \: \\ by \: 5[/tex]
[tex] \frac{5x}{5} < \frac{55}{5} \\ x < 11[/tex]
The required solution of inequality is,
⇒ x < 11
We have to simplify the expression,
⇒ 5 (x + 4) < 75
We can simplify it by definition of inequality as,
⇒ 5 (x + 4) < 75
⇒ 5x + 20 < 75
Subtract 20 both side,
⇒ 5x + 20 - 20 < 75 - 20
⇒ 5x < 55
⇒ 5x - 55 < 0
⇒ 5 (x - 11) < 0
⇒ x - 11 < 0
⇒ x < 11
Therefore, The required solution of inequality is,
⇒ x < 11
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Fiad the sample variance and standard deviation.
21, 10, 3, 7, 11
Answer:
SD = 5.987, Var(X) = 35.85
Step-by-step explanation:
Apply the standard deviation formula, remembering that n represents the sample size. Then, just take the square of the standard deviation to obtain the variance.
Hope this helps!
Please help me with this question, I need it to pass the class!!
Answer:
cos(20°)
Step-by-step explanation:
The "cofunction" is the function having the same value for the complement of the angle that this function has for the angle.
The cofunction of sine is cosine. The complement of 70° is 90° -70° = 20°.
sin(70°) = cos(20°)
Giving a test to a group of students, the grades and gender are summarized below
A B C Total
Male 7 20 14 41
Female 3 4 19 26
Total 10 24 33 67
If one student is chosen at random,
Find the probability that the student was male OR got an "A".
Answer:
46/ 67
Step-by-step explanation:
The numbers of students irrespective of grades is;
The sum of the last roll of numbers:
10+24+ 33+ 67 = 134
The number of males irrespective of grades is the sum of the numbers in the male row ;
7 +20+ 14 +41= 82
The numbers of students with grade A is the first column at the last row and is 10;
Hence;
the probability that the student was male OR got an 'A' is
the probability that the student was male plus the probability that he/she got an 'A'.
The probability that it's a male is ;
Number of males/ total number of students
=82/134
The probability that he got an A is;
The number of students that got A/ the total number of students;
10/134
Hence
the probability that the student was male OR got an 'A' is;
82/ 134 + 10/134 = 92/134 = 46/ 67
sum what is the sum of 199+ -24=
?
Answer:
175
Step-by-step explanation:
+ × - = -
thus 199+(-24)
199-24
175
Answer: 199 + -24 = 175
Step-by-step explanation: 199 is a positive number and -24 is a negative number. If the positive number is bigger than the negative number you subtract. So forget that the - sign is there and subtract it.
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
B. 4x² - 20x + 26
Step-by-step explanation:
→Set it up, like so:
(2x - 5)² + 1
4x² - 20x + 25 + 1
→Add like terms (25 and 1):
4x² - 20x + 26
Assume that random guesses are made for seven multiple choice questions on an SAT test, so that there are n=7 trials, each with probability of success (correct) given by p= 0.2. Find the indicated probability for the number of correct answers.
Find the probability that the number x of correct answers is fewer than 4.
Answer:
Step-by-step explanation:
Let x be a random variable representing the number of guesses made for the sat questions.
Since the probability of getting the correct answer to a question is fixed for any number of trials and the outcome is either getting it correctly or not, then it is a binomial distribution. The probability of success, p = 0.2
Probability of failure, q = 1 - p = 1 - 0.2 = 0.8
the probability that the number x of correct answers is fewer than 4 is expressed as
P(x < 4)
From the binomial distribution calculator,
P(x < 4) = 0.97
A hotel rents 220 rooms at a rate of $ 40 per day. For each $ 1 increase in the rate, two fewer rooms are rented. Find the room rate that maximizes daily revenue. The rate that maximizes revenue is $ .
Answer:
The rooms should be rented at $75 per day for a maximum income of $11250 per day.
Step-by-step explanation:
If the daily rental is increased by $ x
then
Rental: R (x )=( 40 + x ) dollars per room-day
Number of rooms rented: N ( x ) = ( 220 − 2 x ) and
Income: I ( x ) = ( 40 + x ) ( 220 − 2 x ) =8800+140x-2x² dollars/day
The maximum will be achieved when the derivative of I ( x ) is zero.
[tex]\frac{dI(x)}{dx} =140-4x=0[/tex]
x=35
so, ($40+$35)=75$per day
I ( x35) =8800+140(35)-2(35)²= 11250
Im stuck who can help me
Answer:
Option D
Step-by-step explanation:
This question is based on the " Partition Postulate. " You might be familiar with it, it states that a whole is composed of several parts. In this case you could say that this " whole " is ∠ ABC, and the " parts " are ∠1 and ∠2. By this Theorem you could also state the following;
[tex]m< ABC = m< 1 + m< 2,\\\\Substitute,\\110 = 4x + ( 5x + 10 ),\\110 = 4x + 5x + 10,\\4x + 5x + 10 = 110 - Option D\\\\Solution - Option D[/tex]
Hope that helps!
To determine the density of grains, a student uses a 50ml beaker graded by 5ml increments and a scale with 1g absolute uncertainty. The measurement of the volume results in 3 full beakers and 1 beaker filled up to 30ml. Measured mass of a plastic container with all the grains is 185 grams; measured mass of the same container without grains is 65 grams. What is the mass of the grains
Answer:
The mass of the grains = 120 ± 1 g
Step-by-step explanation:
we are given the following:
Total mass of container + grains = 185 grams
Mass of container = 65 grams
Therefore, mass of grains is calculated as follows:
Mass of grains = ( Mass of container + grains) - mass of container
= 185 - 65 = 120 grams.
since the scale has an absolute uncertainty of 1 g, the mass of the grains is written as 120 ± 1 g
Solve Ixl >-9
No solution
All reals
(X|X<-9 or X>9)
Answer:
all reals
Step-by-step explanation:
all reals as |x| >= 0 for every x real
so |x| > -9 is always true
What’s the correct answer for this?
Answer:
B.
Step-by-step explanation:
Since two diameters are intersecting eachother, the angles inside them would be vertical angles so they'll be congruent.
So
m<LYM = m<JYM
Also their arcs would be equal to their angles measures so,
Arc JK = 52°
what equation results from completing the square and then factoring? x^2+24x=33
a.) (x+24)^2=57
b.) (x+12)^2=57
c.) (x+12)^2=177
d.) (x+24)^=177
The factorisation of the given equation using completing square method is (x+12)²=177. Therefore, option D is correct.
The given equation is x²+24x=33.
We need to factorise the equation using completing the square method.
What is completing the square method?Completing the square means writing a quadratic in the form of a squared bracket and adding a constant if necessary.
Now, x²+24x-33=0
Add and subtract (b/2)²=144 to the equation.
x²+24x-33+144-144=0
⇒x²+24x+144-33-144=0
⇒(x+12)²-177=0
⇒(x+12)²=177
The factorisation of the given equation using completing square method is (x+12)²=177. Therefore, option D is correct.
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Find the value of x from this adjoining figure
Answer:
[tex]x=15^\circ[/tex]
Step-by-step explanation:
Please refer to the attached figure for labeling of given diagram:
We are given the following angles:
[tex]\angle AOC = 3x^\circ\\\angle BOD = 2x^\circ\\\angle EOF = 7x^\circ[/tex]
Angles opposite to each other when they are formed by crossing of two lines are known as vertically opposite angles. And vertically opposite angles are always equal to each other.
Using property of vertically opposite angles:
[tex]\angle EOF = \angle AOB = 7x^\circ[/tex]
Line CD is a straight line, so [tex]\angle COD = 180^\circ[/tex]
Also,
[tex]\angle COD = \angle COA+\angle AOB+\angle BOD = 180^\circ\\\Rightarrow 3x + 7x + 2x=180^\circ\\\Rightarrow 12x =180^\circ\\\Rightarrow x = \dfrac{180}{12}\\\Rightarrow x = 15^\circ[/tex]
Hence, answer is [tex]x = 15^\circ[/tex].
Suppose that a company's sales were $1,000,000 6 years ago and are $9,000,000 at the end of the 6 years. Find the geometric mean growth rate of sales. (Round your answer to 4 decimal places.)
Answer:
The geometric mean growth rate of sales is 1.4422.
Step-by-step explanation:
We have two sales values, one from 6 years ago and the other from now.
We have to calculate the geometric growth rate of sales.
We have:
[tex]y(-6)=1,000,000\\\\y(0)=9,000,000[/tex]
We can write the relation between these two values as:
[tex]y(0)=y(-6)k^{0-(-6)}\\\\9,000,000=1,000,000k^6\\\\k^6=9\\\\k=9^{1/6}= 1.4422[/tex]
The geometric mean growth rate of sales is 1.4422.
Abena travelled 40% of the distance of her trip alone, went another 35 miles with Saralyn,
and then finished the last half of the journey alone. How many miles long was the journey?
Answer:
350 miles long.
Step-by-step explanation:
First, we analyze the breakdown of the journey
Abena travelled 40% of the distance of her trip alone.She went 35 miles with Saralyn.She finished the last half (50%) of the journey alone.Let the total distance of the journey =x
Therefore:
10% of the total distance of the journey =35 miles
10% of x=35
0.1x=35
Divide both sides by 0.1
x-350 miles
Therefore, the journey was 350 miles long.
Answer:
The journey was 350 miles long
Step-by-step explanation:
The parameters given are;
Distance traveled by Abena alone = 40% and the last half
∴ Distance traveled by Abena alone = 40% + 50% = 90%
Distance Abena traveled with Saralyn = 35 miles = 100% - 90% = 10%
Hence 10% of Abena's journey = 35 miles
The total distance of Abena's journey therefore, is given as follows
10% = 35 miles
Total distance of Abena's journey = 100% of Abena's journey = 10 × 10%
10 × 10% = 10 × 35 miles = 350 miles
The total distance of Abena's journey = 350 miles.
Donte simplified the expression below. 4(1+3i) - (8-5i)
4 + 3i - 8 + 5i
-4 + 8i
What mistake did donte make?
Answer:
Donde didn't multiply 4(1+3i)
Answer: it’s A he did not apply distributive property yo
Step-by-step explanation:
If theta=3pi/4
Sin theta=?
Cos theta=?
Answer:
For ease of writing, θ [tex]=x[/tex]
[tex]sin(x)=\frac{1}{\sqrt{2} }[/tex]
[tex]cos(x)=-\frac{1}{\sqrt{2} }[/tex]
Step-by-step explanation:
Our angle is [tex]x=\frac{3\pi }{4}[/tex]
To find our answers for [tex]sin(\frac{3\pi}{4} )[/tex] and [tex]cos(\frac{3\pi}{4} )[/tex], we will need to use a unit circle. (I have attached the image of one).
Recall that the [tex]sin[/tex] of an angle is equal to the y-value of the corresponding ordered pair.
And the [tex]cos[/tex] of an angle is equal to the x-value of the corresponding ordered pair.
For the angle [tex]x=\frac{3\pi }{4}[/tex], the ordered pair is [tex](-\frac{1}{\sqrt{2}} }, \frac{1}{\sqrt{2} } )[/tex]
This means that
[tex]sin(x)=\frac{1}{\sqrt{2} }[/tex]
[tex]cos(x)=-\frac{1}{\sqrt{2} }[/tex]
Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Find the probability that a given score is less than negative 1.15−1.15 and draw a sketch of the region.
Answer:
Step-by-step explanation:
Let x be the random variable representing the test scores from the bone density test. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = standard deviation
From the information given,
µ = 0
σ = 1
the probability that a given score is less than negative 1.15 is expressed as
P(x < - 1.15)
z = (- 1.15 - 0)/1 = - 1.15
Looking at the normal distribution table, the probability corresponding to the z score is 0.13
P(x < - 1.15) = 0.13
The sketch of the region is shown in the attached photo
On his way out to meet a friend for lunch, David realized that his financial record was not up to date. He notices that he forgot to record three transactions. The first transaction was on August 2nd in the amount of $12.32, another transaction on that same day in the amount or $52.34, and finally a transaction on August 8th in the amount of $85.35. Determine David's balance carried forward for the 8th of August using the table below and the information provided. A check register. The Balance on August fifth is 1,049 dollars and 16 cents. a. $975.32 b. $899.15 c. $1,049.16 d. $848.84
Answer:
b
Step-by-step explanation:
add the three numbers together then minus from the main total
Answer:
B. $899.15
Step-by-step explanation:
What’s the correct answer for this question?
Answer:
A.
Step-by-step explanation:
Density = Mass / Volume
D = 3/0.2
D = 15 kg/m³
Answer:
density=mass/volume
d=3kg/0.2m3
=15kgm-3
Twice the difference of a number and 4 is equal to three times the sum of the number and 6. Find the number.
The number is
Answer:
-26
Step-by-step explanation:
2(x-4)=3(x+6)
2x-8=3x+18
2x-2x -8 = 3x-2x +18
-8 =X+18
-8-18=x+18-18
-26 = x
The value of the unknown number is -26.
Given that, twice the difference of a number and 4 is equal to three times the sum of the number and 6.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the unknown number x.
Twice the difference of a number and 4 = 2(x-4)
Three times the sum of the number and 6 = 3(x+6)
So, equation is 2(x-4)=3(x+6)
⇒ 2x-8=3x+18
⇒ 3x-2x=-8-18
⇒ x=-26
Therefore, the value of the unknown number is -26.
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A consumer affairs investigator records the repair cost for 4 randomly selected TVs. A sample mean of $91.78 and standard deviation of $23.13 are subsequently computed. Determine the 90% confidence interval for the mean repair cost for the TVs. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answer:
= ( $72.756, $110.804)
Therefore, the 90% confidence interval (a,b) = ( $72.756, $110.804)
Critical value at 90% confidence = 1.645
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean x = $91.78
Standard deviation r = $23.13
Number of samples n = 4
Confidence interval = 90%
Using the z table;
z(α=0.05) = 1.645
Critical value at 90% confidence = 1.645
Substituting the values we have;
$91.78+/-1.645($23.13/√4)
$91.78+/-1.645($11.565)
$91.78+/-$19.024425
$91.78+/-$19.024
= ( $72.756, $110.804)
Therefore, the 90% confidence interval (a,b) = ( $72.756, $110.804)
Evie has two sets of blocks of identical size and shape with the colors given. Evie will randomly select on block from each set. What is the probability she will select an orange block and a red block?
set A has 4 orange blocks and 3 yellow blocks.
set B has 5 blue blocks and 2 red blocks.
3/7
2/7
8/49
6/49
Answer:
[tex]\frac{8}{49}[/tex]
Step-by-step explanation:
Orange: [tex]\frac{4}{7}[/tex]
Red: [tex]\frac{2}{7}[/tex]
[tex]\frac{4}{7} *\frac{2}{7} =\frac{8}{49}[/tex]
In a study investigating the effect of car speed on accident severity, 5000 reports of fatal automobile accidents were examined, and the vehicle speed at impact was recorded for each one. For these 5000 accidents, the average speed was 42 mph and the standard deviation was 15 mph. A histogram revealed that the vehicle speed at impact distribution was approximately normal.
a. Roughly what proportion of vehicle speeds were between 27 and 57 mph?
b. Roughly what proportion of vehicle speeds exceeded 57 mph?
Answer:
(a) Roughly 68% of vehicle speeds were between 27 and 57 mph.
(b) Roughly 16% of vehicle speeds exceeded 57 mph.
Step-by-step explanation:
We are given that in a study investigating the effect of car speed on accident severity, 5000 reports of fatal automobile accidents were examined.
For these 5000 accidents, the average speed was 42 mph and the standard deviation was 15 mph.
Let X = vehicle speed at impact
SO, X ~ Normal([tex](\mu=42,\sigma^{2} = 15^{2}[/tex])
Here, [tex]\mu[/tex] = population average speed = 42 mph
[tex]\sigma[/tex] = standard deviation = 15 mph
Since, the distribution is approximately normal; so the 68-95-99.7 empirical rule states that;
68% of the data values lies within one standard deviation points.95% of the data values lies within two standard deviation points.99.7% of the data values lies within three standard deviation points.(a) Since, it is stated above that 68% of the data values lies within one standard deviation points, that means;
68% data values will lie between [ [tex]\mu-\sigma , \mu+\sigma[/tex] ] , i.e;
[ [tex]\mu-\sigma , \mu+\sigma[/tex] ] = [42 + 15 , 42 - 15]
= [57 , 27]
So, it means that roughly 68% of vehicle speeds were between 27 and 57 mph.
(b) We have observed above that roughly 68% of vehicle speeds were between 27 and 57 mph which leads us to the conclusion that (100% - 68% = 32%) of the data values will be outside this range.
It is stated that of this 32%, half of the data values will be less than 27 mph and half of the data values will be more than 57 mph.
This means that roughly 16% of vehicle speeds exceeded 57 mph.
What’s the correct answer for this?
Answer:
D.
Step-by-step explanation:
Since opposite angles of a quadrilateral inscribes in a circle add up to 180°
So,
<P + <N = 180°
2x+2x-12 = 180°
4x = 180+12
4x = 192
Dividing both sides by 4
x = 48
Now
<P = 2(48)
<P = 96
Now
<N = 2(48)-12
<N = 96-12
<N = 84