36 In determining automobilemileage ratings it was found tha

36/ In determining automobile-mileage ratings, it was found that the mpg (X) for a certain model is nor- mally distributed, with a mean of 33 mpg and a stan dard deviation of 1.7 mpg. Find the following: a. P(X 31) e. The mileage rating that the upper 5% of cars achieve.

Solution

36)

P(X < x) = P(Z < x-mean/std)

a)

P(X < 30) = P(Z < 30 - 33/1.7)

= P(Z < -1.7647) = 0.0403

b)

P(28 < X < 32) = P(X < 32) - P(X < 28)

= P(Z < 32-33/1.7) - P(Z < 28-33/1.7)

= P( Z< -0.58882) - P( Z < -2.94117)

= 0.2782 - 0.0016

= 0.2766

c)

P(X > 35)

= P(Z > 35-33/1.7)

= P(Z > 1.1765)

=0.1197

d)

P(X > 31)

= P(Z > 31-33/1.7)

= P(Z > -1.1765)

= 0.8803

e)

P(X < x) = 1- 0.05

x- 33/1.7 = 1.645

x = 35.80