Question

A population has a mean of 110.22 and a standard deviation of 5.68. For which sample size does 95% of the sample means fall within the interval between 109.08 and 111.36?

a. 100
b.80
c. 60
d. 120

Answer 1

To find the sample size for which 95% of the sample means fall within the given interval, use the formula for the margin of error.

Step-by-step explanation:

To find the sample size for which 95% of the sample means fall within the given interval, we need to use the formula for the margin of error:

Margin of Error = Critical Value * (Standard Deviation / √(Sample Size))

Since we want 95% of the sample means to fall within the interval, the critical value is 1.96 (corresponding to a 95% confidence level). Substituting the given values into the formula, we get:

1.96 = (111.36 - 110.22) / (5.68 / √(Sample Size))

Solving for Sample Size, we find:

Sample Size = (1.96 * (5.68 / (111.36 - 110.22)))^2

Calculating the value, we get approximately 100. Therefore, the correct answer is 100 (option a).

Answer 2

a.100

Step-by-step explanation:

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