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Chapter 7: Q.16 (page 428)

Find the probability that the sum of the 100values is greater than 3,910.

Short Answer

Expert verified

The probability that the sum of the 100 values is greater than 3,910isP(X鈮�3910)=0.0359.

Step by step solution

01

Given Information

From the information given in the question, the mean is 39.01with a standard deviation of 0.5.

02

Explanation

To find the probability that the sum of the 100values is greater than3910:

鈭�X~Nn渭x,n蟽x

鈭�X~N((100)(39.01),(100)(0.5))

P(X鈮�3910)=PZ鈮�X-n渭xn蟽x=PZ鈮�3910-39015=P(Z鈮�1.8)

P(X鈮�3910)=0.0359

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Most popular questions from this chapter

Based on data from the National Health Survey, women between the ages of 18and 24have an average systolic blood pressures (in mm Hg) of 114.8with a standard deviation of 13.1. Systolic blood pressure for women between the ages of 18to 24follow a normal distribution.

a. If one woman from this population is randomly selected, find the probability that her systolic blood pressure is greater than 120.

b. If40women from this population are randomly selected, find the probability that their mean systolic blood pressure is greater than 120.

c. If the sample were four women between the ages of18to 24 and we did not know the original distribution, could the central limit theorem be used?

Yoonie is a personnel manager in a large corporation. Each month she must review 16of the employees. From past experience, she has found that the reviews take her approximately four hours each to do with a population standard deviation of 1.2hours. Let 围 be the random variable representing the time it takes her to complete one review. Assume 围 is normally distributed. Let x-be the random variable representing the meantime to complete the 16reviews. Assume that the 16reviews represent a random set of reviews.

Find the probability that one review will take Yoonie from 3.5to 4.25hours. Sketch the graph, labeling and scaling the horizontal axis. Shade the region corresponding to the probability

b. P(________ <x< ________) = _______

The length of time a particular smartphone's battery lasts follows an exponential distribution with a mean of ten months. A sample of 64 of these smartphones is taken.

Find the IQR for the mean amount of time 64 batteries last.

For the sums of distribution to approach a normal distribution, what must be true?

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

Find the first quartile for the sums.
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