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Chapter 7: Q.7 (page 428)

An unknown distribution has a mean of 80and a standard deviation of 12. A sample size of 95is drawn randomly from the population.

Find the probability that the sum of the 95values is greater than 7650.

Short Answer

Expert verified

The value probability that the sum of 95values is greater than 7650is =0.3345

Step by step solution

01

Given Information

Given in the question that, mean =80

standard deviation is12

Find the probability that the sum of the 95 values is greater than 7,650.

02

Explanation

From the information given in the question, the sample size of 95is randomly drowned from the population with a mean of 80and the standard deviation is 12.

We have to use Ti-83 calculator to find the probability that the totality of 95values is greater than 7650.

For this, click on 2as , then DISTR, and then scroll down to the normal CDF option and enter the supplied details. After this, click on ENTER button on the calculator to have the preferred result.

03

Explanation

The screenshot is given below:

Therefore, the value probability that the sum of 95values is greater than 7650is:

=1-0.66548

=0.3345

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Most popular questions from this chapter

The cost of unleaded gasoline in the Bay Area once followed an unknown distribution with a mean of \(4.59and a standard deviation of \)0.10. Sixteen gas stations from the Bay Area are randomly chosen. We are interested in the average cost of gasoline for the 16gas stations. The distribution to use for the average cost of gasoline for the 16gas stations is:

a.X炉~N(4.59,0.10)

b.X炉~N4.59,0.1016

c.X炉~N4.59,160.10

d.X炉~N4.59,160.10

The mean number of minutes for app engagement by a table use is 8.2 minutes. Suppose the standard deviation is one minute. Take a sample size of 70.

a. What is the probability that the sum of the sample is between seven hours and ten hours? What does this mean in context of the problem?

b. Find the 84thand 16thpercentiles for the sum of the sample. Interpret these values in context.

According to the Internal Revenue Service, the average length of time for an individual to complete (keep records for, learn, prepare, copy, assemble, and send) IRS Form 1040is 10.53hours (without any attached schedules). The distribution is unknown. Let us assume that the standard deviation is two hours. Suppose we randomly sample 36taxpayers.

a. In words, 围=_____________

b. In words,X=_____________

c. X炉~_____(_____,_____)

d. Would you be surprised if the 36taxpayers finished their Form 1040s in an average of more than 12hours? Explain why or why not in complete sentences.

e. Would you be surprised if one taxpayer finished his or her Form 1040in more than 12hours? In a complete sentence, explain why.

A uniform distribution has a minimum of six and a maximum of ten. A sample of 50is taken.

Find P(危x>420).

Determine which of the following are true and which are false. Then, in complete sentences, justify your answers.

a. When the sample size is large, the mean of X炉is approximately equal to the mean of X.

b. When the sample size is large, X炉is approximately normally distributed.

c. When the sample size is large, the standard deviation of X炉is approximately the same as the standard deviation of X.
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