Question 1

Ten percent of graduating college seniors report planning to spend at least one year volunteering for a charitable organization.You interview 30 randomly selected graduating seniors.Assuming that all the binomial conditions are met, determine the probability that no more than 4 students in the group plan to volunteer.

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Question 2

Ten percent of graduating college seniors report planning to spend at least one year volunteering for a charitable organization.You interview 30 randomly selected graduating seniors.Assuming that all the binomial conditions are met, determine the probability that exactly one student in this group of 30 plans to volunteer.

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Question 3

Ten percent of graduating college seniors report planning to spend at least one year volunteering for a charitable organization.You interview 30 randomly selected graduating seniors.Assuming that all the binomial conditions are met, determine the probability that at least three students in the group plan to volunteer.

Accepted Answer

The probability of at least three students planning to volunteer can be calculated using the binomial distribution formula. The probability of success (p) is 0.10, and the number of trials (n) is 30. We calculate the probability of 0, 1, and 2 students planning to volunteer and subtract from 1 to find the probability of at least 3 students. This results in approximately 0.5886.

Question 4

Your car (like most cars) has four tires.Each tire has a 5% chance of running low on air in the morning.Assume that the state of one tire has no relationship to the state of the others.Use the binomial probability function to determine the probability that no more than one tire will be running low on air tomorrow morning.

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Question 5

The most popular names for babies born in the United Kingdom in 2012 were Harry and Amelia.Of the roughly 400,000 baby boys born in the UK in 2012, two percent were named Harry, while two percent of the girls born that year were named Amelia (Source: UK Office for National Statistics, Baby Names, England and Wales, 2012).Suppose that 20 baby boys are chosen at random.Let X represent the number of boys named Harry.What is the standard deviation of X?

Accepted Answer

The standard deviation of a binomial distribution is the square root of np(1-p), where n is the number of trials and p is the probability of success. In this case, n = 20 and p = 0.02, so the standard deviation is sqrt(20 * 0.02 * 0.98) = 0.179.

Question 6

The most popular names for babies born in the United Kingdom in 2012 were Harry and Amelia.Of the roughly 400,000 baby boys born in the UK in 2012, two percent were named Harry, while two percent of the girls born that year were named Amelia (Source: UK Office for National Statistics, Baby Names, England and Wales, 2012).Suppose that 30 baby girls are chosen at random.Let X represent the number of girls named Amelia.What is the expected value of X?

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Question 7

Your car (like most cars) has four tires.Each tire has a 1% chance of running low on air in the morning.Assume that the state of one tire has no relationship to the state of the others.Use the binomial probability function to determine the probability that one tire will be running low on air tomorrow morning.

Accepted Answer

The probability that exactly one tire will be running low on air can be calculated using the binomial probability formula, which is P(X=k) = C(n, k) * p^k * (1-p)^(n-k), where n is the number of trials (in this case, 4 tires), k is the number of successful outcomes (1 tire running low on air), p is the probability of success on a single trial (1% or 0.01), and C(n, k) is the combination of n items taken k at a time. Plugging in the values gives P(1) = C(4, 1) * (0.01)^1 * (0.99)^3 = 4 * 0.01 * 0.970299 = 0.039.

Question 8

Ten percent of graduating college seniors report planning to spend at least one year volunteering for a charitable organization.You interview 30 randomly selected graduating seniors.Assuming that all the binomial conditions are met, determine the probability that between 2 and 5 students in the group plan to volunteer.

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Question 9

Use the Binomial distribution to produce P(x < 12), where n = 15, p = .7.

Accepted Answer

To find $P(x < 12)$ for a binomial distribution with $n = 15$ and $p = 0.7$, we calculate the cumulative probability of getting 0 to 11 successes. The binomial distribution formula is not directly applied here; instead, we use a binomial distribution table or a calculator with binomial distribution functions. Since the exact calculation process isn't shown, we rely on the correct option provided. Among the options, E) .8732 is the most plausible value for $P(x < 12)$ given the parameters, as it suggests a high probability of getting fewer than 12 successes out of 15 trials with a success probability of 0.7 per trial. This aligns with the expected behavior of the binomial distribution under these conditions.

Question 10

Salem University's MBA program has a 55% acceptance rate.You randomly select a sample of 20 applicants.For the random variable "number of applicants in the sample who are accepted into the program," compute the expected value.

Accepted Answer

The expected value for a binomial distribution is calculated as $n \times p$, where $n$ is the number of trials (in this case, 20 applicants) and $p$ is the probability of success (in this case, the acceptance rate of 55% or 0.55). Therefore, the expected value is $20 \times 0.55 = 11$.

Question 11

In recent years, 30% of the patent applications submitted to the US Patent Office have been approved.Assuming that this same rate holds in the future, if 15 new applications are submitted this year, how likely is it that between 11 and 13 (inclusive) applications will be disapproved?

Accepted Answer

The probability of disapproval is 70% (1 - 0.30). Using the binomial probability formula, calculate the probability of 11, 12, and 13 disapprovals out of 15 applications, then sum these probabilities to find the total likelihood.

Question 12

Salem University's MBA program has a 55% acceptance rate.If you randomly select a sample of 20 applicants, how likely is it that between 13 and 17 (inclusive) of the applicants will be accepted into the program?

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Question 13

The most popular names for babies born in the United Kingdom in 2012 were Harry and Amelia.Of the roughly 400,000 baby boys born in the UK in 2012, two percent were named Harry.Two percent of girls born in the UK in 2012 were named Amelia (Source: UK Office for National Statistics, Baby Names, England and Wales, 2012).If thirty boys are selected at random from those born in the UK in 2012, what is the probability that two boys or more in the group will be named Harry?

Accepted Answer

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Question 14

Salem University's MBA program has a 55% acceptance rate.If you randomly select a sample of 20 applicants, how likely is it that 10 of the applicants will be accepted into the program?

Accepted Answer

The likelihood of exactly 10 out of 20 applicants being accepted can be calculated using the binomial probability formula. The correct probability, when calculated, is approximately 0.1593.

Question 15

Car Sounds sells and installs high-end sound systems for cars.10% of the systems that the company installs need to be re-installed because of faulty first-time installation.You plan to randomly select 20 of Car Sounds' recent installations.How likely is it that at least three of these systems will require re-installation.?

Accepted Answer

The probability of a system requiring re-installation is 0.1. The probability of a system not requiring re-installation is 0.9. The probability of at least three systems requiring re-installation is 1 - the probability of 0, 1, or 2 systems requiring re-installation. The probability of 0 systems requiring re-installation is 0.9^20 = 0.1216. The probability of 1 system requiring re-installation is 20 * 0.1 * 0.9^19 = 0.2189. The probability of 2 systems requiring re-installation is 20 * 19 / 2 * 0.1^2 * 0.9^18 = 0.2434. Therefore, the probability of at least three systems requiring re-installation is 1 - 0.1216 - 0.2189 - 0.2434 = 0.3230.

Question 16

Car Sounds sells and installs high-end sound systems for cars.10% of the systems that the company installs need to be re-installed because of faulty first-time installation.You plan to randomly select 20 of Car Sounds' recent installations.How likely is it that the company will have to re-install no more than one of these systems?

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Question 17

Car Sounds sells and installs high-end sound systems for cars.10% of the systems that the company installs need to be re-installed because of faulty first-time installation.You plan to randomly select 20 of Car Sounds' recent installations.In this sample, there's less than a 2% chance that more than what number of the systems will have to be re-installed.

Accepted Answer

10% of 20 is 2, so there's less than a 2% chance that more than 2 of the systems will have to be re-installed.

Question 18

Salem University's MBA program has a 55% acceptance rate.If you randomly select a sample of 20 applicants, how likely is it that no more than five of the applicants in the sample will fail to be accepted into the program?

Accepted Answer

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Question 19

In recent years, 30% of the patent applications submitted to the US Patent Office have been approved.Assuming that this same rate holds in the future, if 15 new applications are submitted this year, how likely is it that at least 9 of them will be disapproved?

Accepted Answer

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Question 20

Salem University's MBA program has a 55% acceptance rate.You randomly select a sample of 20 applicants.For the random variable "number of applicants in the sample who are accepted into the program," compute the standard deviation.

Accepted Answer

The standard deviation for a binomial distribution is calculated using the formula: √(n * p * (1-p)), where n is the number of trials (20 applicants), and p is the probability of success (0.55 acceptance rate). Plugging in the values gives √(20 * 0.55 * 0.45) = 2.23.

Quiz 5: Discrete Probability Distributions

Use the Binomial distribution to produce P(x < 12) , where n = 15, p = .7.

Salem University's MBA program has a 55% acceptance rate.You randomly select a sample of 20 applicants.For the random variable "number of applicants in the sample who are accepted into the program," compute the expected value.

In recent years, 30% of the patent applications submitted to the US Patent Office have been approved.Assuming that this same rate holds in the future, if 15 new applications are submitted this year, how likely is it that between 11 and 13 (inclusive) applications will be disapproved?

Salem University's MBA program has a 55% acceptance rate.If you randomly select a sample of 20 applicants, how likely is it that between 13 and 17 (inclusive) of the applicants will be accepted into the program?

Salem University's MBA program has a 55% acceptance rate.If you randomly select a sample of 20 applicants, how likely is it that 10 of the applicants will be accepted into the program?

Salem University's MBA program has a 55% acceptance rate.If you randomly select a sample of 20 applicants, how likely is it that no more than five of the applicants in the sample will fail to be accepted into the program?

In recent years, 30% of the patent applications submitted to the US Patent Office have been approved.Assuming that this same rate holds in the future, if 15 new applications are submitted this year, how likely is it that at least 9 of them will be disapproved?

Salem University's MBA program has a 55% acceptance rate.You randomly select a sample of 20 applicants.For the random variable "number of applicants in the sample who are accepted into the program," compute the standard deviation.