A population is known to have a standard deviation of 26.1. A sample space of 35 items has a mean of 562. Construct a 90% confidence interval estimate of the name of the population.

553.74≤x≤578.26

Explanation:

The formula for calculating the confidence interval is expressed as

CI = xbar±(z×s/√n)

xbar is the mean = 562

s is the standard deviation = 26.1

n is the sample size = 35

z is the z score at 90% CI = 1.645

Substitute the values into the formula

CI = xbar±(z×s/√n)

CI = 561±(1.645×26.1/√35)

CI = 561±(1.645×4.412)

CI = 561±7.257

CI = {561-7.257, 571+7.257}

CI = {553.74, 578.26}

Hence the 90% confidence interval estimate of the name of the population is 553.74≤x≤578.26

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