Answer:
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:
- Almost all the data lies within three standard deviation from the mean for a normally distributed data.
- About 68.72% of data lies within one standard deviation from the mean.
- About 95.45% of data lies within two standard deviations of the mean.
- About 99.7% of data lies within three standard deviation of the mean.
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