Question 1

You test 4 items from a lot of 15. What is the probability that you will test no defective items if the lot contains 3 defective items?

Accepted Answer

The answer of You test 4 items from a lot...

Question 2

You test 3 items from a lot of 12. What is the probability that you will test no defective items if the lot contains 2 defective items?

Accepted Answer

The answer of You test 3 items from a lot...

Question 3

Suppose a man has ordered twelve 1-gallon paint cans of a particular color (lilac) from the local paint store in order to paint his mother's house. Unknown to the man, three of these cans contains an incorrect mix of paint. For this weekend's big project, the man randomly selects four of these 1-gallon cans to paint his mother's living room. Let x = the number of the paint cans selected that are defective. Unknown to the man, x follows a hypergeometric distribution. Find the mean of this distribution.

Accepted Answer

The mean of a hypergeometric distribution is given by:E(X) = n * (K/N)where:n is the number of drawsK is the number of successes in the populationN is the size of the populationIn this case, n = 4, K = 3, and N = 12. So, the mean is:E(X) = 4 * (3/12) = 1

Question 4

You randomly select 7 students from a class with 15 male and 20 female students. What is the probability that you will choose exactly 4 females?

Accepted Answer

The answer of You randomly select 7 students from a...

Question 5

Given that x is a hypergeometric random variable with N = 9, n = 3, and r = 5, compute the standard deviation of x.

Accepted Answer

The standard deviation of a hypergeometric distribution is calculated using the formula: sqrt(n * (r/N) * ((N-r)/N) * ((N-n)/(N-1))). Plugging in the values N = 9, n = 3, and r = 5, we get the standard deviation as approximately 0.745.

Question 6

Suppose a man has ordered twelve 1-gallon paint cans of a particular color (lilac) from the local paint store in order to paint his mother's house. Unknown to the man, three of these cans contains an incorrect mix of paint. For this weekend's big project, the man randomly selects four of these 1-gallon cans to paint his mother's living room. Let x = the number of the paint cans selected that are defective. Unknown to the man, x follows a hypergeometric distribution. Find the probability that at least one of the four cans selected contains an incorrect mix of paint.

Accepted Answer

The answer of Suppose a man has ordered twelve 1-gallon...

Question 7

Given that x is a hypergeometric random variable with N = 10, n = 5, and r = 6, compute the mean of x.

Accepted Answer

The mean of a hypergeometric distribution is given by the formula: (n * r) / N. Substituting the given values: (5 * 6) / 10 = 3.

Question 8

Given that x is a hypergeometric random variable with N = 8, n = 4, and r = 3, compute the variance of x.

Accepted Answer

The variance of a hypergeometric random variable is given by:Var(X) = (N-n) * n * r * (N-r) / (N^2 * (N-1))Plugging in the given values, we get:Var(X) = (8-4) * 4 * 3 * (8-3) / (8^2 * (8-1)) = .538

Question 9

Suppose a man has ordered twelve 1-gallon paint cans of a particular color (lilac) from the local paint store in order to paint his mother's house. Unknown to the man, three of these cans contains an incorrect mix of paint. For this weekend's big project, the man randomly selects four of these 1-gallon cans to paint his mother's living room. Let x = the number of the paint cans selected that are defective. Unknown to the man, x follows a hypergeometric distribution. Find the standard deviation of this distribution.

Accepted Answer

The standard deviation of a hypergeometric distribution is calculated using the formula: sqrt[n * (k/N) * ((N-k)/N) * ((N-n)/(N-1))], where N is the total number of items, k is the number of defective items, and n is the number of items chosen. Here, N=12, k=3, n=4. Plugging these values into the formula gives approximately 0.739.

Question 10

Suppose a man has ordered twelve 1-gallon paint cans of a particular color (lilac) from the local paint store in order to paint his mother's house. Unknown to the man, three of these cans contains an incorrect mix of paint. For this weekend's big project, the man randomly selects four of these 1-gallon cans to paint his mother's living room. Let x = the number of the paint cans selected that are defective. Unknown to the man, x follows a hypergeometric distribution. Find the probability that none of the four cans selected contains an incorrect mix of paint.

Accepted Answer

The answer of Suppose a man has ordered twelve 1-gallon...

Question 11

Given that x is a hypergeometric random variable with N = 10, n = 5, and r = 6, find each probability. a. P(x = 0) b. P(x = 1) c. P(x ≤ 1) d. P(x ≥ 2)

Accepted Answer

The answer of Given that x is a hypergeometric random...

Question 12

Given that x is a hypergeometric random variable with N = 10, n = 3, and r = 5: a. Display the probability distribution in tabular form. b. Compute μ and σ for x. c. What is the probability that x will fall within the interval μ ± 2σ

Accepted Answer

The answer of Given that x is a hypergeometric random...

Question 13

Given that x is a hypergeometric random variable with N = 8, n = 4, and r = 3: a. Display the probability distribution in tabular form. b. Find P(x ≤ 2).

Accepted Answer

The answer of Given that x is a hypergeometric random...

Quiz 4: Discrete Random Variables

You test 4 items from a lot of 15. What is the probability that you will test no defective items if the lot contains 3 defective items?

You test 3 items from a lot of 12. What is the probability that you will test no defective items if the lot contains 2 defective items?

You randomly select 7 students from a class with 15 male and 20 female students. What is the probability that you will choose exactly 4 females?

Given that x is a hypergeometric random variable with N = 9, n = 3, and r = 5, compute the standard deviation of x.

Given that x is a hypergeometric random variable with N = 10, n = 5, and r = 6, compute the mean of x.

Given that x is a hypergeometric random variable with N = 8, n = 4, and r = 3, compute the variance of x.

Given that x is a hypergeometric random variable with N = 10, n = 5, and r = 6, find each probability. a. P(x = 0) b. P(x = 1) c. P(x ≤ 1) d. P(x ≥ 2)

Given that x is a hypergeometric random variable with N = 10, n = 3, and r = 5: a. Display the probability distribution in tabular form. b. Compute μ and σ for x. c. What is the probability that x will fall within the interval μ ± 2σ

Given that x is a hypergeometric random variable with N = 8, n = 4, and r = 3: a. Display the probability distribution in tabular form. b. Find P(x ≤ 2).