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Chapter 5: Q 5.12. (page 200)

Oklahoma State Officials. Refer to Table 5.1 on page 196.

(a). List the possible samples without replacement of size 3 that can be obtained from the population of five officials. (Hint: There are 10 possible samples.)

If a simple random sample without replacement of three officials is taken from the five officials, determine the probability that

(b). the governor, attorney general, and treasurer are obtained.

(c). the governor and treasurer are included in the sample.

(d). the governor is included in the sample.

Short Answer

Expert verified

Part (a)GLS,GLA,GLT,GAT,GSA,GST,LSA,LST,SAT,LAT

Part (b) 0.1

Part (c) 0.3

Part (c) 0.6

Step by step solution

01

Part (a) Step 1. Given information.

The given statement is:

The given table 5.1 is on page 196 is shown below:

02

Part (a) Step 2. List the possible samples without replacement of size 3 that can be obtained from the population of five officials.

In each sample, only one official can be chosen at a time.

As a result, the following consequences are possible:

GLS,GLA,GLT,GAT,GSA,GST,LSA,LST,SAT,LAT

03

Part (b) Step 1. Determine the probability that the governor, attorney general, and treasurer are obtained if a simple random sample without replacement is taken.

A simple random sample with no replacement is utilized to choose the three of the five officials.

The number of positive outcomes divided by the total number of possible outcomes is the likelihood.

GAT is a possible consequence out of a total of ten possible outcomes.

As a result, a sample of the governor, attorney general, and treasurer has a chance of:

110=0.1.

04

Part (c) Determine the probability that the governor and treasurer are included in the sample.  

Possible outcomes of the probability that the governor and treasurer are:

GLT, GST, GAT

As a result, a sample that includes the governor and treasurer has a probability of:

310=0.3

05

Part (d) Determine the probability that the governor is included in the sample.

Possible outcomes of the probability that the governor and treasurer are:

GLS, GLA, GLT, GAT, GSA, GST

As a result, a sample that includes the governor is included in the sample has a probability of:

610=0.6

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