Question

The typical amount of sleep per night for college graduate students has a normal

distribution with a mean of 5 hours. What is the standard deviation of this distribution if

​16% of students sleep more than 6.5​ hours?

A.

1.52

B.

​-1.55

C.

​-1.52

D.

1.55

Answer 1

Solution:-

Given that,

mean = = 5 hours

x = 6.5 hours

Using standard normal table,

P(Z > z) = 16%

= 1 - P(Z < z) = 0.16  

= P(Z < z) = 1 - 0.16

= P(Z < z ) = 0.84

= P(Z < 0.99 ) = 0.84  

z = 0.99

Using z-score formula,

x = z * +

6.5 = 0.99 * + 5

= 6.5 - 5 / 0.99

= 1.52

correct option is = A