Question

The distribution of a random variable X is symmetric, with a mean of 500 and a standard
Deviation of 10. You are asked to provide two numbers such that about 68% of the values
Of X are between the two numbers. The two numbers are:
a. (400, 600)
b. (490, 510)
c. (480,520)
d. Can’t tell

Answer 1

Given that,

mean = = 500

standard deviation = = 10

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*10+500

x= 490 , 510

correct option b. (490, 510)