Question

X ~ N(60, 12). Suppose that you form random samples of 25 from this distribution. Let

X

be the random variable of averages. Let ΣX be the random variable of sums.

Find the 20th percentile. (Round your answer to two decimal places.)

Answer 1

solution

Given that,

mean = = 60

standard deviation = = 12

n = 25

= 60

= / n = 12/25=2.4

Using standard normal table,

P(Z < z) = 20%

= P(Z < z) = 0.20  

= P(Z < -0.84 ) = 0.20

z = - 0.84    Using standard normal table,

Using z-score formula  

= z * +   

= - 0.84 *2.4+60

= 57.984

= 57.98