Question 1

Approximately 1% of all USPS package deliveries are lost.You select 10 package deliveries at random.If you use the binomial probability function to compute the probability that none of the packages is lost, the value of the binomial coefficient in your computation is

Accepted Answer

The binomial coefficient for computing the probability that none of the packages is lost in 10 trials (n=10) with each trial having two possible outcomes (lost or not lost) is given by "n choose k" where n is the number of trials and k is the number of successful outcomes we are interested in. Here, we are interested in the scenario where none of the packages are lost, so k=0. The binomial coefficient for "10 choose 0" is calculated as 10! / (0! * (10-0)!) = 1. Therefore, the correct answer is 10.00, which is a misunderstanding in the representation. The correct interpretation should be that the binomial coefficient represents the number of ways to choose 0 successes (or failures) out of 10, which is indeed 1, aligning with choice E.

Question 2

For a binomial distribution, find P(3 < x < 5), where n = 15, p = .5.

Accepted Answer

The answer of For a binomial distribution, find P(3 <...

Question 3

Approximately 1% of all USPS package deliveries are lost.You select 10 deliveries at random.Assuming that all the binomial conditions are met, what is the "expected" number of lost packages in this 10 delivery sample?

Accepted Answer

The expected number of lost packages in a binomial distribution is calculated by multiplying the probability of a single event by the number of trials. Here, with a 1% loss rate (0.01) and 10 deliveries, the expected number is 0.01 * 10 = 0.10.

Question 4

For a binomial distribution, find P(x > 2), where n = 10, p = .4.

Accepted Answer

To find P(x > 2) for a binomial distribution with n = 10 and p = 0.4, we calculate 1 - P(x ≤ 2). Using the binomial probability formula or a binomial table/calculator, P(x ≤ 2) is approximately 0.1672. Therefore, P(x > 2) = 1 - 0.1672 = 0.8328.

Question 5

The following probability distribution represents the number of vehicles available for use by a randomly selected US household.To simplify matters, the category "three or more" is replaced by "3" (Source: US Census, American FactFinder).Calculate the standard deviation of the number of vehicles available per household.

Accepted Answer

The answer of The following probability distribution represents the number...

Question 6

It is reported that 23% of the home mortgages in Cowlitz County are "underwater".For 50 randomly selected home mortgages, compute the variance of the random variable "number of underwater mortgages."

Accepted Answer

The answer of It is reported that 23% of the...

Question 7

The following probability distribution represents the number of bedrooms in a randomly selected US household.To simplify matters, the category "five or more" is replaced by "5" (Source: US Census, American FactFinder).Calculate the variance of the number of bedrooms per household.

Accepted Answer

The answer of The following probability distribution represents the number...

Question 8

It is reported that 7% of the Super Star scratch-and-win lottery tickets are winners.If you scratch 250 tickets, what is the expected number of winners?

Accepted Answer

The answer of It is reported that 7% of the...

Question 9

The following probability distribution represents the number of bedrooms in a randomly selected US household.To simplify matters, the category "five or more" is replaced by "5" (Source: US Census, American FactFinder).Calculate the expected value of the number of bedrooms per household.

Accepted Answer

The answer of The following probability distribution represents the number...

Question 10

Five percent of all international video calls on Interphone.com are dropped.Suppose you randomly choose 5 recent calls.If you use the binomial function to compute the probability that exactly 3 of the 5 calls are dropped, what is the value of the binomial coefficient in you computation?

Accepted Answer

The binomial coefficient for choosing exactly 3 calls out of 5 is calculated using the combination formula, which is $C(n, k) = \frac{n!}{k!(n-k)!}$. Here, $n=5$ and $k=3$, so the binomial coefficient is $C(5, 3) = \frac{5!}{3!(5-3)!} = \frac{5 \times 4}{2 \times 1} = 10.0$.

Question 11

It is reported that 23% of the home mortgages in Cowlitz County are "underwater".For 50 randomly selected home mortgages, compute the expected number of underwater mortgages.

Accepted Answer

The expected number of underwater mortgages is calculated by multiplying the probability (23% or 0.23) by the total number of mortgages (50), which equals 11.5.

Question 12

It is reported that 7% of the Super Star scratch-and-win lottery tickets are winners.If you scratch 250 tickets what is the variance of the random variable "number of winners"?

Accepted Answer

The answer of It is reported that 7% of the...

Question 13

Five percent of all international video calls on Interphone.com are dropped.Suppose you randomly choose 5 recent calls.Use the binomial function to compute the probability that no more than two calls are dropped.

Accepted Answer

The probability of no more than two calls being dropped can be calculated using the binomial probability formula, which is P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successful trials, p is the probability of success, and (n choose k) is the binomial coefficient. Here, n = 5 (since 5 calls are chosen), p = 0.05 (since there's a 5% chance of a call being dropped), and we're interested in the probability of k = 0, 1, or 2 calls being dropped.P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)Calculating each term:- P(X = 0) = (5 choose 0) * (0.05)^0 * (0.95)^5 = 1 * 1 * 0.95^5 ≈ 0.7738- P(X = 1) = (5 choose 1) * (0.05)^1 * (0.95)^4 = 5 * 0.05 * 0.95^4 ≈ 0.2036- P(X = 2) = (5 choose 2) * (0.05)^2 * (0.95)^3 = 10 * 0.05^2 * 0.95^3 ≈ 0.0216Adding these probabilities gives P(X ≤ 2) ≈ 0.7738 + 0.2036 + 0.0216 = 0.9990. The closest option to this calculated probability is A) .9988.

Question 14

Five percent of all international video calls on Interphone.com are dropped.Suppose you randomly choose 5 recent calls.Use the binomial function to compute the probability that none of the calls are dropped.

Accepted Answer

The probability that none of the calls are dropped is calculated using the binomial probability formula: P(X=0) = (n choose x) * p^x * (1-p)^(n-x), where n=5, x=0, and p=0.05. This results in approximately 0.7738.

Question 15

For a binomial distribution, find P(x = 2), where n = 8, p = .7.

Accepted Answer

The answer of For a binomial distribution, find P(x =...

Question 16

Julian picks winning and losing stocks by tossing a coin (heads means winner, tails means loser).To test his 'system', his friend gives him a list of 20 stocks, half of which doubled in value over the past 3 years (winners) and half of which lost half their value over the past 3 years (losers).How likely is it that Julian properly classifies at least 80% of the stocks on the list?

Accepted Answer

To properly classify at least 80% of the stocks, Julian needs to correctly identify at least 16 out of 20 stocks. The probability of correctly classifying a stock by tossing a coin is 0.5 (since there's a 50% chance of picking heads for a winner or tails for a loser). The probability of getting at least 16 correct out of 20 can be calculated using the binomial probability formula, but it's a very small chance given the random nature of his method. The correct choice (B) reflects a very low probability, consistent with the difficulty of achieving at least an 80% success rate by random chance.

Question 17

It is reported that 7% of the Super Star scratch-and-win lottery tickets are winners.If you scratch 250 tickets, what is the standard deviation of the random variable "number of winning tickets"?

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 (250 tickets), and p is the probability of success (0.07). Plugging in the values gives √(250 * 0.07 * 0.93) ≈ 4.03.

Question 18

Approximately 1% of all USPS package deliveries are lost.You select 10 package deliveries at random.Use the binomial probability function to compute the probability that no more than one package will be lost.

Accepted Answer

The probability that no more than one package will be lost can be calculated using the binomial probability formula, which is P(X = k) = (nCk) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successful trials, p is the probability of success on a single trial, and nCk is the binomial coefficient. Here, n = 10, p = 0.01 (since 1% of packages are lost), and we want to find the probability of k = 0 or k = 1.For k = 0 (no packages lost): P(X = 0) = (10C0) * (0.01)^0 * (0.99)^10 ≈ 0.9044For k = 1 (one package lost): P(X = 1) = (10C1) * (0.01)^1 * (0.99)^9 ≈ 0.0914Adding these probabilities gives the total probability of no more than one package being lost: 0.9044 + 0.0914 = 0.9958.

Question 19

It is reported that 23% of the home mortgages in Cowlitz County are "underwater".For 50 randomly selected home mortgages, compute the standard deviation of the random variable "number of underwater home mortgages" in the sample of 50.Assume all the binomial conditions are met.

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 (50), and p is the probability of success (0.23). Plugging in the values: √(50 * 0.23 * 0.77) ≈ 2.98.

Question 20

Julian picks winning and losing stocks by tossing a coin (heads means winner, tails means loser).To test his 'system', his friend gives him a list of 20 stocks, half of which doubled in value over the past 3 years (winners) and half of which lost half their value over the past 3 years (losers).How likely is it that Julian properly classifies at least 60% of the stocks on the list?

Accepted Answer

The answer of Julian picks winning and losing stocks by...

Quiz 5: Discrete Probability Distributions

Approximately 1% of all USPS package deliveries are lost.You select 10 package deliveries at random.If you use the binomial probability function to compute the probability that none of the packages is lost, the value of the binomial coefficient in your computation is

For a binomial distribution, find P(3 < x < 5) , where n = 15, p = .5.

Approximately 1% of all USPS package deliveries are lost.You select 10 deliveries at random.Assuming that all the binomial conditions are met, what is the "expected" number of lost packages in this 10 delivery sample?

For a binomial distribution, find P(x > 2) , where n = 10, p = .4.

It is reported that 23% of the home mortgages in Cowlitz County are "underwater".For 50 randomly selected home mortgages, compute the variance of the random variable "number of underwater mortgages."

The following probability distribution represents the number of bedrooms in a randomly selected US household.To simplify matters, the category "five or more" is replaced by "5" (Source: US Census, American FactFinder) .Calculate the variance of the number of bedrooms per household.

It is reported that 7% of the Super Star scratch-and-win lottery tickets are winners.If you scratch 250 tickets, what is the expected number of winners?

The following probability distribution represents the number of bedrooms in a randomly selected US household.To simplify matters, the category "five or more" is replaced by "5" (Source: US Census, American FactFinder) .Calculate the expected value of the number of bedrooms per household.

Five percent of all international video calls on Interphone.com are dropped.Suppose you randomly choose 5 recent calls.If you use the binomial function to compute the probability that exactly 3 of the 5 calls are dropped, what is the value of the binomial coefficient in you computation?

It is reported that 23% of the home mortgages in Cowlitz County are "underwater".For 50 randomly selected home mortgages, compute the expected number of underwater mortgages.

It is reported that 7% of the Super Star scratch-and-win lottery tickets are winners.If you scratch 250 tickets what is the variance of the random variable "number of winners"?

Five percent of all international video calls on Interphone.com are dropped.Suppose you randomly choose 5 recent calls.Use the binomial function to compute the probability that no more than two calls are dropped.

Five percent of all international video calls on Interphone.com are dropped.Suppose you randomly choose 5 recent calls.Use the binomial function to compute the probability that none of the calls are dropped.

For a binomial distribution, find P(x = 2) , where n = 8, p = .7.

It is reported that 7% of the Super Star scratch-and-win lottery tickets are winners.If you scratch 250 tickets, what is the standard deviation of the random variable "number of winning tickets"?

Approximately 1% of all USPS package deliveries are lost.You select 10 package deliveries at random.Use the binomial probability function to compute the probability that no more than one package will be lost.

It is reported that 23% of the home mortgages in Cowlitz County are "underwater".For 50 randomly selected home mortgages, compute the standard deviation of the random variable "number of underwater home mortgages" in the sample of 50.Assume all the binomial conditions are met.