Use the area to find the radius. If you could include steps that’ll be very helpful :)
Answers
Answer:
Area = PI * radius^2
radius^2 = Area / PI
radius^2 = 169*PI/PI
radius^2 = 169
radius = 13
Step-by-step explanation:
Related Questions
Which graph represents viable values for y = 2x, where x is the number of pounds of rice scooped and purchased from a bulk bin at the grocery store and y is the total cost of the rice? On a coordinate plane, a straight line with a positive slope begins at point (0, 0), and ends at point (2.5, 5). On a coordinate plane, blue diamonds appear at points (0, 0), (1, 2), (2, 4). On a coordinate plane, a straight line with a positive slope begins at point (negative 2.5, negative 5), crosses the x- and y-axis at point (0, 0), and ends at point (2.5, 5). On a coordinate plane, blue diamonds appear at points (negative 2, negative 4), (negative 1, negative 2), (0, 0), (1, 2), (2, 4). Mark this and return
Answers
Answer:
On a coordinate plane, a straight line with a positive slope begins at point (0, 0), and ends at point (2.5, 5)
Step-by-step explanation:
The distinction between "straight line" and "blue diamonds" is that the straight line represents the relation for all possible values of x. The blue diamonds show the values of y for very specific values of x.
Since x is the amount of rice from a bulk bin, we assume it can take any non-negative value. Hence, the graphs with negative values or with "blue diamonds" are not appropriate.
The straight-line graph in the first quadrant is the best choice.
Answer:
The answer is graph 1
Step-by-step explanation:
On a coordinate plane, a straight line with a positive slope begins at point (0, 0), and ends at point (2.5, 5).
Please help me with this question!!!!
Answers
Answer:
-3i +-12j
Step-by-step explanation:
P2 -P1 = (-1-2, -6-6) = (-3, -12)
In terms of unit vectors i and j, this is -3i -12j.
What’s the correct answer for this question?
Answers
Answer:
A.
Step-by-step explanation:
Volume of cone = 1/3πr²h
= (1/3)(3.14)(1.5)²(5)
= (1/3)(3.14)(2.25)(5)
= (1/3)(35.3)
= 11.78
≈ 11.8 cubic inches
A car travels 300 miles in 10 hours at a constant rate. If the distance traveled by the car can be represented as a function of
the time spent driving, what is the value of the constant of variation, K?
O 1/30 mph
30 mph
60 mph
3000 mph
Answers
Answer:
30 mph
Step-by-step explanation:
Distance travelled=300 miles
Time travelled=10hours
At a constant rate,k
Let distance travelled=d
Time travelled=t
Then,
d=kt
300=k*10
300=10k
k=300/10
=30
k=30mph
30 miles per hour
30 MPH ............................................................................................................
Given the following data, find the weight that represents the 53rd percentile.
Weights of Newborn Babies9.4 7.5 5.4 7.5 7.1
6.0 8.1 5.7 7.1 6.6
9.4 5.8 8.7 5.7 9.3
Answers
Answer:
Step-by-step explanation:
Rearranging the weights in ascending order, it becomes
5.4, 5.7, 5.7, 5.8, 6.0, 6.6, 7.1, 7.1, 7.5, 7.5, 8.1, 8.7, 9.3, 9.4, 9.4
The formula for determining the percentile is expressed as
n = (P/100)N
Where
n represents the value of the given percentile
P represents the given percentile
N represents the number of items(weights)
From the information given, the number of items, n is 15
P = 53
Therefore,
n = (53/100) × 15
n = 7.95
n = 8
Therefore, the weight that represents the 53rd percentile is the 8th value. It becomes 7.1
53rd percentile is 7.1
Which of the following is the solution to |x-1|=8
Answers
Answer:
-7,9
Step-by-step explanation:
x-1=-8
x=-7
x-1=8
x=9
What are the terms in the algebraic expression
102 + 10 +
3b
Answers
Answer:
102, 10, and, 3b
Step-by-step explanation:
Which undefined term is used to define an angle
Answers
Answer:
The undefined term which is used to define an angle is line i.e., . Further explanation: In geometry the three terms which are considered to be undefined are line, point and plane.
Answer:
Line
Step-by-step explanation:
A line is a undefined term used to define a angle. An angle is the corner that is created where two non-parallel lines meet/ intersect
Using a 40% solution, make 100 mL of a 10% solution?
Answers
Answer:
I don't know
Step-by-step explanation:
but that looks like chemistry not biology
helpppppppppppppppppppppppppppppppppp
Answers
Answer:
answer is 2/3
Step-by-step explanation:
probability it is an eclair is 1/15=3/(3+2x+6+x)= 1/(x+3)
so x+3=15 and then x = 12
so the probability it is a humbug is (2*12+6)/(3*12+9) = 30/45 = 2/3
NEED HELP ASAP
Solve the equation or inequality for the unknown number. Show your work.
Answers
Answer:
5
Step-by-step explanation:
3(14+x) = 57
42 +3x = 57
3x = 15
x = 5
The volume of a triangular prism is increased by a factor of 8.
By what factor is the surface area of the figure increased?
o 2
o 4
016
o 24
Answers
i believe that is the right answer
Ben bought 4 volleyballs and 5 footballs for $352.65 altogether. If Ben’s brother bought 2 volleyballs and 4 footballs for $249.12 altogether, what was the price of each football?
Answers
Answer:
$48.53
Step-by-step explanation:
The purchases can be written in equation form as ...
4v +5f = 352.65
2v +4f = 249.12
Doubling the second equation and subtracting the first gives ...
2(2v +4f) -(4v +5f) = 2(249.12) -(352.65)
3f = 145.59 . . . . simplify
f = 48.53 . . . . . . divide by 3
The price of each football was $48.53.
Michelle purchased a sofa that was on sale for $125 off. The original price of the sofa was $515. What was the sale price of the sofa?
Answers
Answer:
We know that:
The original price was $515
and
It was $125 off
so we need to find the price of the sofa after the discount.
$515 - $125 = $390
The sale price of the sofa after the discount was $390
hope This helps and pls mark me brainliest if it did :)
If the size of the sample to be used in a particular test of attributes has not been determined by utilizing statistical concepts, but the sample has been chosen in accordance with random selection procedures
A) No inferences can be drawn from the sample.
B) The auditor has committed a nonsampling error.
C) The auditor may or may not achieve the desired risk of assessing control risk too low.
D) The auditor will have to evaluate the results by reference to the principles of discovery sampling.
E) The auditor may or may not achieve the desired
Answers
Answer:
C) The auditor may or may not achieve the desired risk of assessing control risk too low.
Step-by-step explanation:
In a concept of risk sampling, if the sample size is chosen randomly in accordance with random selection procedures, the auditor may or may not achieve the desired risk of assessing risk too low. In other words the auditor may or may not achieve desired precision. This is because a samole chosen randomly may not represent the true population.
This depends largely on the sample size. If the sample size selected is too small, the allowance for sampling risk will be larger than what is required because it will lead to a large standard error of the mean
Removing which point from the coordinate plane would make the graph a function of x? On a coordinate plane, points are at (negative 2, negative 3), (negative 2, 1), (negative 4, 3), (0, 4), (1, 1), and (2, 3). (–4, 3) (–2, 1) (0, 4) (1, 1)
Answers
Answer:
(-2, 1)
Step-by-step explanation:
For a relation consisting of (x, y) pairs to be a function, all of the x-values must be unique. In the given relation, points (-2, -3) and (-2, 1) have the same x-value. Removing either point will make the relation a function.
Of these, the only one listed among answer choices is (-2, 1).
Answer:
-2 , 1
Step-by-step explanation:
good luck love
Will mark brainliest! Thanks ! and like if you can please explain it cuz I want to understand it to :)
Answers
Answer: F.) 7 triangles
Step-by-step explanation:
Congruent means completely equal in side lengths and angles. Think of this weird figure like 4 triangles that are see through and are covering a diamond underneath
Of those 4 "see through triangles", there are 3 equal to ΔABC
Now on the diamond underneath, there is another 4. Its hard to actually explain what I mean, but take two triangles from that dimaond. Theyre gonna be congruent to ΔABC.
That's 4 + 3 = 7 total triangles
Six measurements were made of the magnesium ion concentration (in parts per million, or ppm) in a city's municipal water supply, with the following results. It is reasonable to assume that the population is approximately normal. Based on a 95% confidence interval for the mean magnesium ion concentration, is it reasonable to believe that the mean magnesium ion concentration may be greater than 199.5? (Hint: you should first calculate the 95% confidence interval for the mean magnesium ion concentration.)
a) The likelihood cannot be determined
b) Yes
c) No
Answers
Answer:
Option B is correct.
It is reasonable to believe that the mean magnesium ion concentration may be greater than 199.5 as the confidence interval obtained contains values that are greater than 199.5
Step-by-step explanation:
Complete Question
Six measurements were made of the magnesium ion concentration (in parts per million, or ppm) in a city's municipal water supply, with the following results. It is reasonable to assume that the population is approximately normal.
170 201 199 202 173 153
Based on a 95% confidence interval for the mean magnesium ion concentration, is it reasonable to believe that the mean magnesium ion concentration may be greater than 199.5? (Hint: you should first calculate the 95% confidence interval for the mean magnesium ion concentration.)
A) The likelihood cannot be determined.
B) Yes
C) No
Solution
For this question, obtaining the confidence interval will give a clear solution to the problem.
Since the Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence, if the range obtained contains values greater than the standard we are comparing against (199.5), then the confidence interval proves that the mean magnesium ion may be greater than 199.5.
But to obtain the confidence interval, we need the mean and standard deviation for the sample.
170, 201, 199, 202, 173, 153
Mean = (sum of variables)/(total number of variables)
Sum of variables = 170+201+199+202+173+153 = 1098
Total number of variables = 6
Mean = (1098/6) = 183
Standard deviation = σ = √[Σ(x - xbar)²/N]
x = each variable
xbar = mean = 183
N = number of variables = 6
Σ(x - xbar)² = (170-183)² + (201-183)² + (199-183)² + (202-183)² + (173-183)² + (153-183)²
= 169 + 324 + 256 + 361 + 100 + 900
= 2110
σ = √(2110/6) = 18.75
Mathematically,
Confidence Interval = (Sample mean) ± (Margin of error)
Sample Mean = 183
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error of the mean)
Critical value will be obtained using the t-distribution. This is because there is no information provided for the population mean and standard deviation.
To find the critical value from the t-tables, we first find the degree of freedom and the significance level.
Degree of freedom = df = n - 1 = 6 - 1 = 5.
Significance level for 95% confidence interval
(100% - 95%)/2 = 2.5% = 0.025
t (0.025, 5) = 2.57 (from the t-tables)
Standard error of the mean = σₓ = (σ/√n)
σ = standard deviation of the sample = 18.75
n = sample size = 6
σₓ = (18.75/√6) = 7.656
95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]
CI = 183 ± (2.57 × 7.656)
CI = 183 ± 19.675
95% CI = (163.325, 202.675)
95% Confidence interval = (163.3, 202.7)
It is reasonable to believe that the mean magnesium ion concentration may be greater than 199.5 as the confidence interval obtained contains values that are greater than 199.5
Hope this Helps!!!
Identify the type of sampling that is used: A list of all registered voters in a state is given to a researcher who would like to determine if a particular candidate is likely to be elected. The researcher has a computer randomly generate several hundred numbers, and those numbers are used to select names from the list to form a sample. a. systematic b. random c. convenience d. stratified
Answers
Answer:
The correct option is (b) random.
Step-by-step explanation:
A simple random sample is a part of a statistical population in which every individual of the population has an equal probability of being selected.
Assigning each individual of the population a unique number and using a computer or random number generator for selection is a procedure to select a simple random sample.
In this case the researcher has a computer randomly generate several hundred numbers, and those numbers are used to select names from the list to form a sample.
The procedure indicates that the researcher used a simple random sampling technique to select the sample.
Thus, the correct option is (b).
A sample is taken from all college freshman . Right-handed students are excluded.what is this an example of?
Answers
Answer:
All college freshman is called Population and Right handed students are excluded is called sample from Population
Step-by-step explanation:
Explanation:-
Population:- The total of the observations which we are concerned
given data all college freshman is called Population
Sample :-
A sample is a subset of a Population
Given data all college freshman is called Population and Right handed students are excluded is called sample from Population
Determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear system. [Start 2 By 3 Matrix 1st Row 1st Column 1 2nd Column 4 3rd Column negative 2 2nd Row 1st Column 3 2nd Column h 3rd Column negative 6 EndMatrix ]
Answers
Answer:
Step-by-step explanation:
Consider the augments matrix (the right most column is the extra vector).
[tex]\left[\begin{matrix} 1 & 4 & -2 \\3 & h & -6\end{matrix}\right][/tex]
By multypling the first row by 3 and substracting it from the second row and saving the result in the second row we get the matrix
[tex]\left[\begin{matrix} 1 & 4 & -2 \\0 & h-12 & 0\end{matrix}\right][/tex]
Note that since the value of the third column in the second row is 0, any value of h gives us a consistent system. An inconsistent system is when we get a row of zeros that is equal to a number different from 0.
For 120 consecutive days, a process engineer has measured the temperature of champagne bottles as they are made ready for serving. Each day, she took a sample of 8 bottles. The average across all 960 bottles (120 days, 8 bottles per day) was 46 degrees Fahrenheit. The standard deviation across all bottles was 0.8 degree.Round your answer to 4 digits after the decimal point if it is not an integer. Do NOT use comma in your numeric answers.Sample size is .Number of samples is .When constructing a x-bar chart:The center line should be .ESD(x-bar) equals .The upper control limit (UCL) should be .The lower control limit (LCL) should be .
Answers
Answer:
Center line = 46
UCL = 46.84852
LCL = 45.15148
Step-by-step explanation:
Given:
Standard deviation = 0.8
Mean, u = 46
Sample size, n= 8
First calculate the estimated standard deviation:
[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{0.8}{\sqrt{8}} = 0.282843[/tex]
a) The center line, X', would be the average across all components. Here the average across all 960 bottles is 46
Therefore,
[tex] X' = 46 [/tex]
b) The upper control limit, UCL:
UCL = u + 3s
= 46 + 3(0.28284)
= 46 + 0.84852
= 46.84852
c) The upper control limit, LCL:
LCL = u + 3s
= 46 - 3(0.28284)
= 46 - 0.84853
= 45.15148
Homework: Section 1.2 Applications Linear
Score: 0 of 1 pt
8 of 10 (7 complete)
1.2.31
How many quarts of pure antifreeze must be added to 4 quarts of a 10% antifreeze solution to obtain a 20% antifreeze solution?
quart(s) of pure antifreeze must be added.
(Round to the nearest tenth as needed)
Answers
Answer:
q = 0.5 quarts of 100% antifreeze
Step-by-step explanation:
q = quarts of pure antifreeze
Set this up as a weighted combination of the mixtures.
(100%)(q) + (10%)(4) = (20%)(q + 4)
100q + 40 = 20(q + 4)
5q + 2 = q + 4
4q = 2
q = 0.5 quarts of 100% antifreeze
I earn $12.00 in 5 hours. At this rate, how many hours will it take to earn $19.20?
Answers
Answer:
8 hours
Step-by-step explanation:
Solve with a proportion
[tex]\frac{12}{5}[/tex] = [tex]\frac{19.20}{x}[/tex]
Multiply 5 by 1.6 to get x
5 x 1.6 = 8
The diagram shows a rectangle and a square.
Diagram
accuratel
The rectangle is 2 cm long and 6 cm wide.
The perimeter of the rectangle is the same as the perimeter of the square.
Work out the length of one side of the square.
Answers
Answer:
4 cm
Step-by-step explanation:
The side of the square will be the average of the two sides of the rectangle with the same perimeter.
Formulas for the perimeters are ...
P = 2(L+W)
P = 4s
Equating these gives ...
4s = 2(L+W)
s = (L +W)/2 . . . . . divide by 4
For the given side lengths, ...
s = (2 cm +6 cm)/2 = (8/2) cm = 4 cm
The length of one side of the square is 4 cm.
Is (-3,2) a solution of 7x+9y>-3
Yes or no
Please help :))
Answers
Answer:
(-3,2) is not a solution.
Step-by-step explanation:
The solution of a linear inequality in two variables like [tex]Ax + By > C[/tex] is an ordered pair [tex](x, y)[/tex] that produces a true statement when the values of x and y are substituted into the inequality.
To find if (-3,2) is a solution of [tex]7x+9y>-3[/tex], you must substitute this point into the inequality.
[tex]7\left(-3\right)+9\left(2\right)>-3\\\\-21+18>-3\\\\-3>-3[/tex]
Because -3 is not greater than -3, (-3,2) is not a solution.
Answer:
No
Step-by-step explanation:
Khan academy
Angelina read 30% of her book containing 360 pages. How many pages has she read so far
Answers
Answer:
108 pages
Step-by-step explanation:
Angelina read 30% of the book that contains 360 pages.
30% of 360 pages
"of" also means multiply, so we must multiply 30% and 360.
30% * 360
Convert 30% to a decimal. Divide 30 by 100, or move the decimal place 2 spots to the left.
30/100=0.30
or
30.0---> 3.0---> 0.30
Plug the decimal in for the percent.
0.30*360
Multiply the 2 numbers together
108
Angelina has read 108 pages so far.
Based on aâ poll, among adults who regret gettingâ tattoos, 18â% say that they were too young when they got their tattoos. Assume that eight adults who regret getting tattoos are randomlyâ selected, and find the indicated probability. Complete partsâ (a) throughâ (d) below.
a. Find the probability that none of the selected adults say that they were too young to get tattoos.
b. Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos.
c. Find the probability that the number of selected adults saying they were too young is 0 or 1.
d. It we randomly select 9 adults. Is 1 a significantly low number who day that they were too young to get tattoos?
Answers
Answer:
a) 20.44% probability that none of the selected adults say that they were too young to get tattoos.
b) 35.90% probability that exactly one of the selected adults says that he or she was too young to get tattoos.
c) 56.34% probability that the number of selected adults saying they were too young is 0 or 1.
d) No
Step-by-step explanation:
For each adult, there are only two possible outcomes. Either they say they were too young when they got their tattoos, or they don't say that. Each adult is independent of each other. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
18% say that they were too young when they got their tattoos.
This means that [tex]p = 0.18[/tex]
Eight adults who regret getting tattoos are randomly selected
This means that [tex]n = 8[/tex]
a. Find the probability that none of the selected adults say that they were too young to get tattoos.
This is P(X = 0).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{8,0}.(0.18)^{0}.(0.82)^{8} = 0.2044[/tex]
20.44% probability that none of the selected adults say that they were too young to get tattoos.
b. Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos.
This is P(X = 1).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{8,1}.(0.18)^{1}.(0.82)^{7} = 0.3590[/tex]
35.90% probability that exactly one of the selected adults says that he or she was too young to get tattoos.
c. Find the probability that the number of selected adults saying they were too young is 0 or 1.
Either a. or b.
20.44 + 35.90 = 56.34
56.34% probability that the number of selected adults saying they were too young is 0 or 1.
d. It we randomly select 9 adults. Is 1 a significantly low number who day that they were too young to get tattoos?
Now [tex]n = 9[/tex]
It is significantly low if it is more than 2.5 standard deviations below the mean.
The mean is [tex]E(X) = np = 9*0.18 = 1.62[/tex]
The standard deviation is [tex]\sqrt{V(X)} = \sqrt{n*p*(1-p)} = \sqrt{9*0.18*0.82} = 1.15[/tex]
1 > (1.62 - 2.5*1.15)
So the answer is no.
In a certain city district the need for money to buy drugs is stated as the reason for 70% of all thefts. Find the probability that among the next 7 theft cases reported in this district, exactly 3 of them resulted from the need to buy drugs.
Answers
Answer:
9.72% probability that among the next 7 theft cases reported in this district, exactly 3 of them resulted from the need to buy drugs.
Step-by-step explanation:
For each theft, there are only two possible outcomes. Either the need to buy drugs is the reason of the theft, or it is not. Each theft is independent of each other. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
In a certain city district the need for money to buy drugs is stated as the reason for 70% of all thefts.
This means that [tex]p = 0.7[/tex]
Find the probability that among the next 7 theft cases reported in this district, exactly 3 of them resulted from the need to buy drugs.
This is P(X = 3) when n = 7. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{7,3}.(0.7)^{3}.(0.3)^{4} = 0.0972[/tex]
9.72% probability that among the next 7 theft cases reported in this district, exactly 3 of them resulted from the need to buy drugs.
Blood types: The blood type o negative is called the "universal donor" type, because it is the only blood type that may safely be transfused into any person
Therefore, when someone needs a transfusion in an emergency and their blood type cannot be determined, they are given type o negative blood. For this
reason, donors with this blood type are crucial to blood banks. Unfortunately, this blood type is fairly rare; according to the Red Cross, only 7% of U.S.
residents have type o negative blood. Assume that a blood bank has recruited 18 donors. Round the answers to four decimal places
Part 1 of 3
(a) What is the probability that three or more of them have type o negative blood?
The probability that three or more of them have type o negative blood is
х
Part 2 of 3
(b) What is the probability that fewer than five of them have type o negative blood?
The probability that fewer than five of them have type o negative blood is
х
Part 3 of
(©) Would it be unusual f none of the donors had type o negative blood?
be unusual if none of the donors had type o negative blood since the probability is
X
It choose one) Y
would
would not
Answers
Answer:
a) The probability that fewer than five of them have type o negative blood is 0.1275
b) The probability that fewer than five of them have type o negative blood is 0.9933
c) 0.2708 probability of no donors with type o negative blood. This probability is higher than 0.05, so it would not be unusual having none of the donors with type o negative blood.
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they have type o negative blood, or they do not. The probability of a person having type o negative blood is independent of any other person. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
7% of U.S. residents have type o negative blood.
This means that [tex]p = 0.07[/tex]
18 donors.
This means that [tex]n = 18[/tex]
(a) What is the probability that three or more of them have type o negative blood?
Either less than three have, or at least three do. The sum of the probabilities of these events is 1. So
[tex]P(X < 3) + P(X \geq 3) = 1[/tex]
We want [tex]P(X \geq 3)[/tex]
So
[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]
In which
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{18,0}.(0.07)^{0}.(0.93)^{18} = 0.2708[/tex]
[tex]P(X = 1) = C_{18,1}.(0.07)^{1}.(0.93)^{17} = 0.3669[/tex]
[tex]P(X = 2) = C_{18,2}.(0.07)^{2}.(0.93)^{16} = 0.2348[/tex]
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2708 + 0.3669 + 0.2348 = 0.8725[/tex]
[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - 0.8725 = 0.1275[/tex]
The probability that fewer than five of them have type o negative blood is 0.1275
(b) What is the probability that fewer than five of them have type o negative blood?
[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{18,0}.(0.07)^{0}.(0.93)^{18} = 0.2708[/tex]
[tex]P(X = 1) = C_{18,1}.(0.07)^{1}.(0.93)^{17} = 0.3669[/tex]
[tex]P(X = 2) = C_{18,2}.(0.07)^{2}.(0.93)^{16} = 0.2348[/tex]
[tex]P(X = 3) = C_{18,3}.(0.07)^{3}.(0.93)^{15} = 0.0942[/tex]
[tex]P(X = 4) = C_{18,4}.(0.07)^{4}.(0.93)^{14} = 0.0266[/tex]
[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.2708 + 0.3669 + 0.2348 + 0.0942 + 0.0266 = 0.9933[/tex]
The probability that fewer than five of them have type o negative blood is 0.9933.
c) Would it be unusual f none of the donors had type o negative blood?
[tex]P(X = 0) = C_{18,0}.(0.07)^{0}.(0.93)^{18} = 0.2708[/tex]
0.2708 probability of no donors with type o negative blood. This probability is higher than 0.05, so it would not be unusual having none of the donors with type o negative blood.