Question

Pets. Refer to Problem 40.

(a) Draw a probability histogram for the random variable X.

(b) The selection of the four households was done without replacement. Strictly speaking, then, why is the probability distribution that you obtained in Problem 40(b) only approximately correct? What is the exact distribution called?

(c) Do you think the probability distribution that you obtained is a reasonable approximation to the actual one? Explain your answer.

Short answer

Part (a)

Part (b) hyper geometric distribution.

Part (c) Yes.

Step-by-step solution

Step 1. Given information.

The given statement is:

Refer to Problem 40. and draw a probability histogram for the random variable X.

Part (a) Step 2. Draw a probability histogram for the random variable X.  

To make a probability histogram using MINITAB.

Procedure for MINITAB:

Choose Graph > Bar Chart as the first step.

Step 2: Select Values from a table based on what the bars represent.

Step 3: Select Simple under One column of values. Select OK.

Step 4: In the Graph variables section, type the column of

Step 5: Fill in the X column in the Categorical variable.

Step 6: Click the OK button.

Step 7: Go to the Scale tab and select the horizontal axis.

Step 8: Type 0 in the Gap between clusters field.

Step 9: Click the OK button.

MINITAB OUTPUT:

Part (b) Step 1. The probability distribution of four households was done without replacing any of them.

The hypergeometric distribution is a type of probability distribution.

The real distribution is a hyper geometric distribution based on sampling without replacement.

Furthermore, depending on the sample, the likelihood of success is roughly 0.60.

Part (c) Step 1. Justify that the obtained probability distribution is a good approximation of the real one.

Yes. Because the sample size does not exceed 5% of the population, the probability distribution produced in part (a) is an acceptable approximation to the actual one.