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Identify the symmetrical interval that includes​ 95% of the sample means for a population with a...

Identify the symmetrical interval that includes​ 95% of the sample means for a population with a mean equal to 51 and a standard deviation equal to 12 using a sample size of 36. What is the lower bound and upper bound of this interval?

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Answer #1

Solution :

Given that,

Z/2 = Z0.025 = 1.96

Margin of error = E = Z/2 * ( /n)

= 1.96 * ( 12 /  36 )

= 3.92

At 95% confidence interval estimate of the population mean is,

  ± E   

51  ± 3.92

= ( 47.08, 54.92 )

Lower bound = 47.08

Upper bound = 54.92

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