The amount of time it takes on an exam is normally distributed with a mean of 72 minutes and standard deviation 4 minutes. Suppose you take a random sample of 64 students from this population. There would be a 99.7% chance that the sample mean amount of time taken on the exam would be between:

A. 68 and 76 minutes
B. 71 and 73 minutes
C. 70.5 and 73.5 minutes
D. 60 and 84 minutes

Option C) 70.5 and 73.5 minutes

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 72 minutes

Standard Deviation, σ = 4 minutes

Sample size, n = 64

We are given that the distribution of amount of time is a bell shaped distribution that is a normal distribution.

Empirical Formula:

Standard error due to sampling =

Thus, by empirical formula 99.7% of data will lie between:

There would be a 99.7% chance that the sample mean amount of time taken on the exam would be between 70.5 and 73.5 minutes.

Thus, the correct answer is

Option C) 70.5 and 73.5 minutes

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step-by-step explanation:

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