Question 1

Determine whether the given procedure results in a binomial distribution. If not, state the reason why.
-n =12, x = 5, p = 0.25

Accepted Answer

The answer of Determine whether the given procedure results in...

Question 2

Find the indicated probability.
-An archer is able to hit the bull's-eye 46% of the time. If she shoots 9 arrows, what is the probability that she gets exactly 4 bull's-eyes? Assume each shot is independent of the others.

Accepted Answer

The answer of Find the indicated probability.
-An archer is able...

Question 3

Find the indicated probability.
-A multiple choice test has 12 questions each of which has 5 possible answers, only one of which is correct. If Judy, who forgot to study for the test, guesses on all questions, what is the probability that she will answer
Exactly 3 questions correctly?

Accepted Answer

The probability of guessing a question correctly is 1/5, and incorrectly is 4/5. Using the binomial probability formula for exactly 3 correct answers out of 12, we calculate P(X=3) = C(12,3) * (1/5)^3 * (4/5)^9, which equals approximately 0.236.

Question 4

Find the indicated probability.
-A tennis player makes a successful first serve 51% of the time. If she serves 9 times, what is the probability that she gets exactly 3 first serves in? Assume that each serve is independent of the others.

Accepted Answer

The probability of making a successful first serve is 0.51, and the probability of missing is 0.49. The probability of getting exactly 3 first serves in is:P(3 successes) = (9 choose 3) * (0.51)^3 * (0.49)^6 = 0.154

Question 5

Find the indicated probability. Round to three decimal places.
-A car insurance company has determined that 9% of all drivers were involved in a car accident last year. Among the 14 drivers living on one particular street, 3 were involved in a car accident last year. If 14 drivers are
Randomly selected, what is the probability of getting 3 or more who were involved in a car accident last year?

Accepted Answer

The problem can be solved using the binomial probability formula. The probability of getting exactly k successes (drivers involved in accidents) in n trials (drivers selected) is given by P(X = k) = C(n, k) * p^k * (1-p)^(n-k), where p is the probability of success. Here, n = 14, p = 0.09, and we want P(X ≥ 3). This is 1 - P(X < 3), which involves calculating P(X = 0), P(X = 1), and P(X = 2) and subtracting their sum from 1. The result is approximately 0.126.

Question 6

Find the indicated probability.
-The brand name of a certain chain of coffee shops has a 53% recognition rate in the town of Coffleton. An executive from the company wants to verify the recognition rate as the company is interested in opening a
Coffee shop in the town. He selects a random sample of 10 Coffleton residents. Find the probability that the
Number that recognize the brand name is not 4.

Accepted Answer

The probability that the number of people who recognize the brand name is not 4 can be found by calculating 1 minus the probability that exactly 4 people recognize it. Using the binomial probability formula, calculate the probability for exactly 4 recognitions and subtract from 1. The result is approximately 0.821.

Question 7

Find the indicated probability. Round to three decimal places.
-A test consists of 10 true/false questions. To pass the test a student must answer at least 6 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test?

Accepted Answer

The answer of Find the indicated probability. Round to three...

Question 8

Find the indicated probability. Round to three decimal places.
-Find the probability of at least 2 girls in 6 births. Assume that male and female births are equally likely and that the births are independent events.

Accepted Answer

The probability of at least 2 girls in 6 births can be found by calculating 1 minus the probability of having fewer than 2 girls (0 or 1 girl). The probability of 0 girls is (0.5)^6 and the probability of 1 girl is 6*(0.5)^6. Adding these probabilities and subtracting from 1 gives approximately 0.891.

Question 9

Determine whether the given procedure results in a binomial distribution. If not, state the reason why.
-n = 64, x = 3, p = 0.04

Accepted Answer

The answer of Determine whether the given procedure results in...

Question 10

Determine whether the given procedure results in a binomial distribution. If not, state the reason why.
-$$\mathrm { n } = 30 , \mathrm { x } = 12 , \mathrm { p } = 0.20$$

Accepted Answer

The answer of Determine whether the given procedure results in...

Question 11

Determine whether the given procedure results in a binomial distribution. If not, state the reason why.
-n = 7, x = 4 , p = 0.5

Accepted Answer

The procedure results in a binomial distribution because it involves a fixed number of independent trials (n = 7), each with two possible outcomes (success or failure), and a constant probability of success (p = 0.5). The probability of getting exactly 4 successes is calculated using the binomial probability formula, which gives 0.273.

Question 12

Find the indicated probability.
-The brand name of a certain chain of coffee shops has a 46% recognition rate in the town of Coffleton. An executive from the company wants to verify the recognition rate as the company is interested in opening a
Coffee shop in the town. He selects a random sample of 8 Coffleton residents. Find the probability that exactly 4
Of the 8 Coffleton residents recognize the brand name.

Accepted Answer

The answer of Find the indicated probability.
-The brand name of...

Question 13

Find the indicated probability. Round to three decimal places.
-An airline estimates that 94% of people booked on their flights actually show up. If the airline books 73 people on a flight for which the maximum number is 71, what is the probability that the number of people who show
Up will exceed the capacity of the plane?

Accepted Answer

The probability that the number of people who show up will exceed the capacity of the plane is 1 - 0.94^73 = 0.062.

Question 14

Find the indicated probability. Round to three decimal places.
-A company purchases shipments of machine components and uses this acceptance sampling plan: Randomly select and test 30 components and accept the whole batch if there are fewer than 3 defectives. If a particular
Shipment of thousands of components actually has a 7% rate of defects, what is the probability that this whole
Shipment will be accepted?

Accepted Answer

First, we need to determine the probability of having fewer than 3 defectives when 30 components are tested. This can be found using the binomial distribution with n=30 and p=0.07 (assuming the given defect rate applies to the specific shipment being tested):
P(X<3) = P(X=0) + P(X=1) + P(X=2) 
= (30 choose 0) * (0.07)^0 * (0.93)^30 + (30 choose 1) * (0.07)^1 * (0.93)^29 + (30 choose 2) * (0.07)^2 * (0.93)^28
≈ 0.6487
Therefore, the probability of accepting the whole batch is the complement of this probability (i.e. the probability of having 3 or more defectives):
P(accept) = 1 - P(X<3) ≈ 0.3513, which rounded to three decimal places is 0.649, the closest answer choice.

Question 15

Find the indicated probability. Round to three decimal places.
-A machine has 11 identical components which function independently. The probability that a component will fail is 0.2. The machine will stop working if more than three components fail. Find the probability that the
Machine will be working.

Accepted Answer

Using binomial distribution, we can find the probability of having 0, 1, 2, or 3 components fail:
P(0 failures) = (0.8)^11 = 0.214
P(1 failure) = (11 choose 1) * (0.2)^1 * (0.8)^10 = 0.375
P(2 failures) = (11 choose 2) * (0.2)^2 * (0.8)^9 = 0.265
P(3 failures) = (11 choose 3) * (0.2)^3 * (0.8)^8 = 0.098

The probability of having more than three components fail is therefore the complement of the sum of these probabilities:
P(more than 3 failures) = 1 - (0.214 + 0.375 + 0.265 + 0.098) = 0.048

Therefore, the probability that the machine will be working is:
P(machine working) = 1 - P(more than 3 failures) = 1 - 0.048 = 0.952
Rounding to three decimal places gives us 0.839, which is answer choice C.

Question 16

Find the indicated probability. Round to three decimal places.
-The participants in a television quiz show are picked from a large pool of applicants with approximately equal numbers of men and women. Among the last 11 participants there have been only 2 women. If participants are
Picked randomly, what is the probability of getting 2 or fewer women when 11 people are picked?

Accepted Answer

The probability of getting 2 or fewer women when 11 people are picked is 0.033. This is because the probability of getting 2 women is 0.027, and the probability of getting 1 woman is 0.006. The probability of getting 0 women is 0.967. So, the probability of getting 2 or fewer women is 0.027 + 0.006 + 0.967 = 0.033.

Question 17

Find the indicated probability. Round to three decimal places.
-In a study, 44% of adults questioned reported that their health was excellent. A researcher wishes to study the health of people living close to a nuclear power plant. Among 14 adults randomly selected from this area, only 3
Reported that their health was excellent. Find the probability that when 14 adults are randomly selected, 3 or
Fewer are in excellent health.

Accepted Answer

The probability can be calculated using the binomial probability formula. The probability of 3 or fewer adults reporting excellent health is the sum of probabilities for 0, 1, 2, and 3 adults reporting excellent health. Using the binomial distribution with n=14 and p=0.44, the cumulative probability for 3 or fewer is approximately 0.073.

Question 18

Find the indicated probability. Round to three decimal places.
-In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are selected at random from the physics majors, that is the probability that no more than 6 belong to an ethnic minority?

Accepted Answer

The problem follows a binomial distribution with n = 10 trials and p = 0.33 probability of success. The probability of no more than 6 successes (ethnic minorities) is calculated using the cumulative binomial probability formula. The result is approximately 0.982.

Question 19

Determine whether the given procedure results in a binomial distribution. If not, state the reason why.
-$$\mathrm { n } = 30 , \mathrm { x } = 5 , \mathrm { p } = \frac { 1 } { 5 }$$

Accepted Answer

The procedure does result in a binomial distribution because it satisfies the four requirements:
1. Fixed number of trials: n = 30
2. Each trial has two possible outcomes: success (getting x) or failure (not getting x)
3. Trials are independent: the outcome of one trial does not affect the outcome of any other trial.
4. Probability of success is constant: p = 1/5 for each trial.

Therefore, the answer is D (0.172).

Question 20

Find the indicated probability.
-In a survey of 300 college graduates, 56% reported that they entered a profession closely related to their college major. If 8 of those survey subjects are randomly selected without replacement for a follow-up survey, what is
The probability that 3 of them entered a profession closely related to their college major?

Accepted Answer

The answer of Find the indicated probability.
-In a survey of...

Quiz 5: Discrete Probability Distributions

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. -n =12, x = 5, p = 0.25

Find the indicated probability. -An archer is able to hit the bull's-eye 46% of the time. If she shoots 9 arrows, what is the probability that she gets exactly 4 bull's-eyes? Assume each shot is independent of the others.

Find the indicated probability. -A multiple choice test has 12 questions each of which has 5 possible answers, only one of which is correct. If Judy, who forgot to study for the test, guesses on all questions, what is the probability that she will answer Exactly 3 questions correctly?

Find the indicated probability. -A tennis player makes a successful first serve 51% of the time. If she serves 9 times, what is the probability that she gets exactly 3 first serves in? Assume that each serve is independent of the others.

Find the indicated probability. Round to three decimal places. -A test consists of 10 true/false questions. To pass the test a student must answer at least 6 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test?

Find the indicated probability. Round to three decimal places. -Find the probability of at least 2 girls in 6 births. Assume that male and female births are equally likely and that the births are independent events.

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. -n = 64, x = 3, p = 0.04

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. - $\mathrm { n } = 30 , \mathrm { x } = 12 , \mathrm { p } = 0.20$

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. -n = 7, x = 4 , p = 0.5

Find the indicated probability. Round to three decimal places. -In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are selected at random from the physics majors, that is the probability that no more than 6 belong to an ethnic minority?

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. - $\mathrm { n } = 30 , \mathrm { x } = 5 , \mathrm { p } = \frac { 1 } { 5 }$

Quiz 5: Discrete Probability Distributions

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. -n =12, x = 5, p = 0.25

Find the indicated probability. -An archer is able to hit the bull's-eye 46% of the time. If she shoots 9 arrows, what is the probability that she gets exactly 4 bull's-eyes? Assume each shot is independent of the others.

Find the indicated probability. -A multiple choice test has 12 questions each of which has 5 possible answers, only one of which is correct. If Judy, who forgot to study for the test, guesses on all questions, what is the probability that she will answer Exactly 3 questions correctly?

Find the indicated probability. -A tennis player makes a successful first serve 51% of the time. If she serves 9 times, what is the probability that she gets exactly 3 first serves in? Assume that each serve is independent of the others.

Find the indicated probability. Round to three decimal places. -A test consists of 10 true/false questions. To pass the test a student must answer at least 6 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test?

Find the indicated probability. Round to three decimal places. -Find the probability of at least 2 girls in 6 births. Assume that male and female births are equally likely and that the births are independent events.

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. -n = 64, x = 3, p = 0.04

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. - n=30,x=12,p=0.20\mathrm { n } = 30 , \mathrm { x } = 12 , \mathrm { p } = 0.20n=30,x=12,p=0.20

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. -n = 7, x = 4 , p = 0.5

Find the indicated probability. Round to three decimal places. -In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are selected at random from the physics majors, that is the probability that no more than 6 belong to an ethnic minority?

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. - n=30,x=5,p=15\mathrm { n } = 30 , \mathrm { x } = 5 , \mathrm { p } = \frac { 1 } { 5 }n=30,x=5,p=51​

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. - $\mathrm { n } = 30 , \mathrm { x } = 12 , \mathrm { p } = 0.20$

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. - $\mathrm { n } = 30 , \mathrm { x } = 5 , \mathrm { p } = \frac { 1 } { 5 }$