Question

Suppose x has a distribution with μ = 33 and σ = 16.

Find P(29 ≤ x ≤ 34). (Round your answer to four decimal places.)

Answer 1

Solution:

Given: x has a distribution with μ = 33 and σ = 16.

We have to find: P(29 ≤ x ≤ 34).

We will assume Normal distribution to find this probability:

Thus find z scores for x= 29 and for x = 34

and

Thus we get:

P(29 ≤ x ≤ 34) = P( -0.25 < Z < 0.06 )

P(29 ≤ x ≤ 34) = P(Z < 0.06 ) - P( Z < -0.25 )

Look in z table for z = 0.0 and 0.06 as well as for z = -0.2 and 0.05 and find corresponding area.

P( Z< 0.06 )= 0.5239

and

P( Z< -0.25) = 0.4013

Thus

P(29 ≤ x ≤ 34) = P(Z < 0.06 ) - P( Z < -0.25 )

P(29 ≤ x ≤ 34) = 0.5239 - 0.4013

P(29 ≤ x ≤ 34) = 0.1226