Question

The heights of a group of girls are normally distributed with a mean of 66 inches. If 95% of the heights of these girls are between 63 and 69 inches, what is the standard deviation for this group.

Answer 1

Answer:

The standard deviation is 1.5 inches.

Step-by-step explanation:

For a normal curve, we have that the area between the mean and the mean plus two times the standard deviation is something around 47.5%

Then the area between the mean minus two times the standard deviation and the mean plus two times the standard deviation is equal to the 95%.

the mean is 66

if the standard deviation is x, we have that:

66 + 2*x = 69

66 - 2*x = 63

then we can find that:

2*x = 66 - 63 = 3

x = 3/2 = 1.5

The standard deviation is 1.5 inches.