Question

Based on tests of a certain automobile, engineers have found that the miles per gallon in highway driving are normally distributed, with a mean of 31 miles per gallon and a standard deviation of 3.4 miles per gallon. 12 of these automobiles are randomly selected and the miles per gallon for each car are recorded.

What is the probability that the mean miles per gallon of this sample exceeds 33 miles per gallon?

Would this be considered unusual?

Answer 1

Solution :

Given that,

mean = = 31

standard deviation = = 3.4

n=12

= =31

= / n =3.4 / 12 = 0.9815

P( >33 ) = 1 - P( <33 )

= 1 - P[( - ) / < (33-31) / 0.9815]

= 1 - P(z <2.04 )

Using z table

= 1 - 0.9793

=0.0207

probability= 0.0207