Question 1

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 2

Given that x is a hypergeometric random variable with N = 8, n = 4, and r = 3, compute the variance of x.
A).732
B).469
C).700
D).538

Accepted Answer

The variance of a hypergeometric distribution is calculated using the formula: Var(X) = n * (r/N) * ((N-r)/N) * ((N-n)/(N-1)). Substituting the given values: Var(X) = 4 * (3/8) * (5/8) * (4/7) = 0.538.

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 motherʹs house. Unknown to the man, three of these cans contains
An incorrect mix of paint. For this weekendʹs big project, the man randomly selects four of these
1-gallon cans to paint his motherʹs 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.
A)1
B)12
C)3
D)4

Accepted Answer

The mean of a hypergeometric distribution is given by $ \mu = \frac{N_r}{N} \times n $, where $N_r$ is the number of successes in the population, $N$ is the population size, and $n$ is the sample size. Here, $N_r = 3$ (defective cans), $N = 12$ (total cans), and $n = 4$ (cans chosen). Thus, $ \mu = \frac{3}{12} \times 4 = 1$.

Question 4

Given that x is a hypergeometric random variable with N = 9, n = 3, and r = 5, compute the standard deviation of x.
A).456
B).745
C).208
D).556

Accepted Answer

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

Question 5

Given that x is a hypergeometric random variable with N = 10, n = 5, and r = 6, compute the mean of x.
A)1
B)4
C)2
D)3

Accepted Answer

The mean of a hypergeometric random variable is given by the formula $ \mu = n\frac{r}{N} $. Substituting the given values, we get $ \mu = 5\frac{6}{10} = 3 $.

Question 6

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

Accepted Answer

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

Question 7

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 motherʹs house. Unknown to the man, three of these cans contains
An incorrect mix of paint. For this weekendʹs big project, the man randomly selects four of these
1-gallon cans to paint his motherʹs 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.
A)0.545
B)1
C)0.739
D)0.297

Accepted Answer

The standard deviation of a hypergeometric distribution is given by the formula: $\sqrt{\frac{N - n}{N - 1} \cdot \frac{nK(N-K)}{N^2}}$, where $N$ is the total number of items, $n$ is the number of items chosen, $K$ is the total number of items with the desired characteristic, and $N-K$ is the number of items without the desired characteristic. Plugging in the values from the problem ($N=12$, $n=4$, $K=3$, $N-K=9$), we get the standard deviation as 0.739.

Question 8

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. $P ( x \leq 1 )$
d. $P ( x \geq 2 )$

Accepted Answer

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

Question 9

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 10

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 $\mu$ and $\sigma$ for $x$.
c. What is the probability that $x$ will fall within the interval $\mu \pm 2 \sigma$

Accepted Answer

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

Question 11

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 motherʹs house. Unknown to the man, three of these cans contains
An incorrect mix of paint. For this weekendʹs big project, the man randomly selects four of these
1-gallon cans to paint his motherʹs 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.
A)0.25455
B)0.50909
C)0.01818
D)0.21818

Accepted Answer

The probability that none of the four cans selected contains an incorrect mix of paint is calculated using the hypergeometric distribution formula. With 9 correct cans and 3 incorrect ones, the probability is approximately 0.25455.

Question 12

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 motherʹs house. Unknown to the man, three of these cans contains
An incorrect mix of paint. For this weekendʹs big project, the man randomly selects four of these
1-gallon cans to paint his motherʹs 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.
A)0.74545
B)0.50909
C)0.78182
D)0.49091

Accepted Answer

The probability that at least one of the four cans selected contains an incorrect mix of paint is 0.74545. This is calculated using the hypergeometric distribution formula, considering the total number of defective cans, the total number of cans, and the number of cans selected.

Question 13

As part of a promotion, both you and your roommate are given free cellular phones from a batch of 13 phones. Unknown to you, four of the phones are faulty and do not work. Find the probability
That one of the two phones is faulty.
A).077
B).231
C).538
D).462

Accepted Answer

The probability that one of the two phones is faulty can be calculated by considering the total ways to choose one faulty phone and one working phone out of the total, divided by the ways to choose any two phones out of the total. There are 4 faulty phones and 9 working phones. The number of ways to choose one faulty and one working phone is 4*9 = 36. The total number of ways to choose any two phones out of 13 is 13C2 = (13*12)/(2*1) = 78. Therefore, the probability is 36/78 = 0.461538, which rounds to 0.462.

Question 14

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...

Quiz 4: Discrete Random Variables

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?

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 = 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: a. Display the probability distribution in tabular form. $\text { b. Find } P ( x \leq 2 ) \text {. }$

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. $P ( x \leq 1 )$ d. $P ( x \geq 2 )$

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 = 10, n = 3, and r = 5: a. Display the probability distribution in tabular form. b. Compute $\mu$ and $\sigma$ for $x$ . c. What is the probability that $x$ will fall within the interval $\mu \pm 2 \sigma$

As part of a promotion, both you and your roommate are given free cellular phones from a batch of 13 phones. Unknown to you, four of the phones are faulty and do not work. Find the probability That one of the two phones is faulty.

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?

Quiz 4: Discrete Random Variables

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?

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 = 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: a. Display the probability distribution in tabular form. b. Find P(x≤2). \text { b. Find } P ( x \leq 2 ) \text {. } b. Find P(x≤2).

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

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 = 10, n = 3, and r = 5: a. Display the probability distribution in tabular form. b. Compute μ\muμ and σ\sigmaσ for xxx . c. What is the probability that xxx will fall within the interval μ±2σ\mu \pm 2 \sigmaμ±2σ

As part of a promotion, both you and your roommate are given free cellular phones from a batch of 13 phones. Unknown to you, four of the phones are faulty and do not work. Find the probability That one of the two phones is faulty.

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?

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

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. $P ( x \leq 1 )$ d. $P ( x \geq 2 )$

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 $\mu$ and $\sigma$ for $x$ . c. What is the probability that $x$ will fall within the interval $\mu \pm 2 \sigma$