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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

Use the information in Example \(7.9\), but change the sample size to \(144\).

a. Find \(P(20<\bar{x}<30)\).

b. Find \(P(\sum x\) is at least \(3,000)\).

c. Find the \(75th\) percentile for the sample mean excess time of \(144\) customers.

Complete the distributions.

a.X~ _____(_____,_____)

b. role="math" localid="1648618952256" X炉~_____(_____,_____)

64. Suppose that a category of world-class runners is known to run a marathon ( 26 miles) in an average of 145 minutes with a standard deviation of 14 minutes. Consider 49 of the races. Let X-be the average of the 49 races.

a. role="math" localid="1652281768411" X-~(___)

b. Find the probability that the runner will average between 142 and 146 minutes in these 49 marathons.

c. Find the 80th percentile for the average of these 49 marathons.

d. Find the median of the average running times.

The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36and a standard deviation of about ten. Suppose that 16individuals are randomly chosen. Let role="math" localid="1648361500255" X炉=average percent of fat calories.

a. X炉~_____ (______, ______)

b. For the group of 16, find the probability that the average percent of fat calories consumed is more than five. Graph the situation and shade in the area to be determined.

c. Find the first quartile for the average percent of fat calories.

A manufacturer produces 25-pound lifting weights. The lowest actual weight is 24 pounds, and the highest is 26 pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of 100 weights is taken.

Find the 90th percentile for the total weight of the 100 weights.
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