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Use the given information to construct a 95% confidence interval estimate of the mean of the population. n = 62, σ = 11.4, = 102.1

A. 101.7 < μ < 102.5

B. 66.1 < μ < 138.1

C. 100.7 < μ < 103.5

D. 99.3 < μ < 104.9

1 Answer

5 votes

Answer:


99.3<\mu<104.9

Therefore, option D is correct.

Explanation:

We have been given
n=62,\sim=11.4\text{and}\bar{x}=102.1

The formula to find interval is:
\mu which is unknown mean.


\bar{x}\pm(\sim)/(√(n))\cdot \text{z-score}

So, 95% confidence interval is standard value of z-score at 95% confidence interval is 1.96

Substituting the values in the formula we will get:


102.1/pm(11.4)/(√(62))(1.96)

On simplifying the above equation we will get:

Taking
102.1-(11.4)/(√(62))(1.96)=99.26≈99.3

and
102.1+(11.4)/(√(62))(1.96)=104.93

Therefore, option D is correct.


99.3<\mu<104.9


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