Question

11. 7 & 8 (S 7.2) Suppose the random variable X follows a normal distribution with mean ?=103and standard deviation ?=25.

Calculate each of the following.

In each case, round your response to at least 2 decimal places.

a) Calculate the location of the 86th percentile on the distribution of X.

b) Calculate the location of the 31st percentile on the distribution of X.

Answer 1

Solution:

Given that,

mean = = 103

standard deviation = = 25

Using standard normal table,

a ) P(Z < z) = 86%

P(Z < z) = 0.86

P(Z < 1.08 ) = 0.86

z = 1.08

Using z-score formula,

x = z * +

x = 1.08 * 25 + 103 = 132.5

x = 132.50

b ) P(Z < z) = 31%

P(Z < z) = 0.31

P(Z < - 0.4959 ) = 0.31

z = - 0.4959

Using z-score formula,

x = z * +

x = 0.4959 * 25 + 103 = 90.6025

x = 90.60