Question

Find the maximum of x in the bottom quartile. (Round your answer to four decimal places.) X ~ N(5, 9)

Answer 1

Solution:-

Given that,

mean = = 5

variance = ² = 9

standard deviation = = 9 = 3

Using standard normal table,

The z dist'n First quartile is,

P(Z < z) = 25%

= P(Z < z) = 0.25  

= P(Z < -0.6745 ) = 0.25

z = -0.6745

Using z-score formula,

x = z * +

x = -0.6745 * 3 + 5

x = 2.9765

First quartile =Q1 = 2.9765