Question

The average February temperature in Indiana is normally distributed with a mean of 28.89 degree and a variance of 26.16 degree (X~N(28.89,26.16)). The average February 2017 temperature is 42.85 degree. What is the probability that the average February temperature is greater than 42.85 degree?

Answer choices:

a. 2.53

b. .0057

c. .9943

d. .7019

Answer 1

Solution:

Given

µ = 28.89

σ = Sqrt(26.16) = 5.114685

We have to find P(X>42.85)

P(X>42.85) = 1 – P(X<42.85)

Z = (Xbar - µ)/σ

Z = (42.85 - 28.89)/5.114685

Z = 2.729396

P(Z<2.729396) = 0.9943

(by using z-table)

P(X>42.85) = 1 – P(X<42.85)

P(X>42.85) = 1 – 0.9943

P(X>42.85) = 0.0057

Answer:

b. .0057