Statistics Question

Question

Given the notation X~N(54,8). Find the following: (round a to 4 decimal places and b to 2 decimal places)

 

a) P(x<30)

 

b) 80th percentile

a) P(x<30) = b) 80th percentile=

Answer 1

part A)

P(X<30) = P( z < (30-54)/8)

= P( z < -24/8)

= P (z < -3)

= 0.00135

= 0.135%

part B)

By REVERSE table lookup,

needs Zk such that:

Prob(z < Zk) = 0.80

Zk= 0.841621234

X= Zk * stndDev + mean

= 0.841621234 * 8 + 54

= 60.732969872