Question

Out of 2,000 random but normally distributed numbers with a mean of 45 and a standard deviation of x, approximately 1,360 numbers are found to be between 40 and 50. What is the value of x? A. 5 B. 10 C. -5 D. 680

Answer 1

A. 5

Explanation:

It says that the sample is normally distributed, which means it follows the bell curve in terms of spreading. That means that 68% of the numbers are within two standard deviations, centered on the mean, one standard deviation below, one up.

That's confirmed by the fact that 1,360 numbers (exactly 68% of 2,000) are between 40 and 50. Since the mean is 45, that gives a spread of ± 1 standard deviation for 68% of the numbers.

One standard deviation goes from 40 to 45, another from 45 to 50.

So, the standard deviation of this sample is 5.