Question

A normal distribution has a mean of 50 and a standard deviation of 12. 68% of the distribution can be found between what two numbers?

Select one:

a. 38 and 62

b. 44 and 56

c. 16 and 86

d. 42 and 58

Answer 1

solution

Given that,

mean = = 50

standard deviation = = 12

middle 68% of score is

P(-z < Z < z) = 0.68

P(Z < z) - P(Z < -z) = 0.68

2 P(Z < z) - 1 = 0.68

2 P(Z < z) = 1 + 0.68 = 1.68

P(Z < z) =1.68 / 2 = 0.84

P(Z < 0.99) = 0.84

z  ± 0.99 using z table

Using z-score formula  

x= z * +

x= ±0.99*12+50

x= 38 and 62