Middle School

Use the given information to construct a 95% confidence interval estimate of the mean of the population. Given: \( n = 62 \), \( \sigma = 11.4 \), \( \bar{x} = 102.1 \).

Choose the correct confidence interval:

A. \( 101.7 < \mu < 102.5 \)

B. \( 66.1 < \mu < 138.1 \)

C. \( 100.7 < \mu < 103.5 \)

D. \( 99.3 < \mu < 104.9 \)

Answer :

Answer:

[tex]99.3<\mu<104.9[/tex]

Therefore, option D is correct.

Step-by-step explanation:

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

The formula to find interval is:[tex]\mu[/tex] which is unknown mean.

[tex]\bar{x}\pm\frac{\sim}{\sqrt{n}}\cdot \text{z-score}[/tex]

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:

[tex]102.1/pm\frac{11.4}{\sqrt{62}}(1.96)[/tex]

On simplifying the above equation we will get:

Taking [tex]102.1-\frac{11.4}{\sqrt{62}}(1.96)=99.26≈99.3[/tex]

and [tex]102.1+\frac{11.4}{\sqrt{62}}(1.96)=104.93[/tex]

Therefore, option D is correct.

[tex]99.3<\mu<104.9[/tex]


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