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Chapter 7: Q.8 (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 less than 7400.

Short Answer

Expert verified

The probability that the sum of the 95values is less than 7400is .

P(X鈮�7400)=0.0436

Step by step solution

01

Given Information

Given in the question that,

mean is 80and the standard deviation is 12and sample size is95

Find the probability that the sum of the 95values is less than 7400.

02

Explanation

From Example, we have the next information

鈭�X~N(n渭x,n蟽x)

鈭�X~N((95)(80),(95)(12))

Now, we can find the probability that the sum of the 95values is less than 7400

P(X鈮�7400)=P(Z鈮�X鈭�n渭xn蟽x)=P(Z鈮�7400鈭�7600116.961532)=P(Z鈮�鈭�1.71)

P(X鈮�7400)=0.0436

03

Explanation

The following is obtained graphically,

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