Question

Out of 2000 random but normally distributed numbers with a mean of 45 and a standard deviation of x, approximately 1360 numbers are found to be between 40 and 50. What is the value of x?

Answer 1

First we have to find which percent of 2000 numbers are 1360 numbers.
p = 1360 / 2000 * 100 = 68 %
It means that for normal distribution the values 40 and 50 are within +/- 1 standard deviation from the mean ( 45 ).
45 - x = 40 and 45 + x = 50.
x = 45 - 40 = 50 - 45 = 5
Answer:
x = 5