Question

A variable X follows a normal distribution with mean 20 and standard deviation 3. Approximately 95% of the distribution can be found between what values of X?

Select one:

a. 10 and 30

b. 17 and 23

c. 0 and 23

d. 14 and 26

e. 18 and 22

Answer 1

Solution:-

Given that,

mean = = 20

standard deviation = = 3

Using standard normal table,

P( -z < Z < z) = 95%

= P(Z < z) - P(Z <-z ) = 0.95

= 2P(Z < z) - 1 = 0.95

= 2P(Z < z) = 1 + 0.95

= P(Z < z) = 1.95 / 2

= P(Z < z) = 0.975

= P(Z < 1.96 ) = 0.975

= z  ± 1.96

Using z-score formula,

x = z * +

x = -1.96 * 3 + 20

x = 14.12

x = 14

Using z-score formula,

x = z * +

x = 1.96 * 3 + 20

x = 25.88

x = 26

The middle 95% are from 14 and 26

correct option is = d