Question

2. The highway fuel economy of cars is normally distributed with a mean of 35 mpg and a standard deviation of 3 mpg.
(A) Ten cars are sampled. How many do you expect to get at most 33 mpg? (9 points)
(B) Ten cars are sampled. What is the probability the mean is at most 33 mpg? (9 points)
(C) A Ford Explorer gets 30 mpg. Is this unusual? Solve with two different (VALID) methods. (18 points)

Show work and excel formulas

Answer 1

The highway fuel economy of cars is normally distributed with

A)

The proportion of cars that you can expect to get at most 33 mpg =

using excel formula NORM.S.DIST(-0.6667, TRUE)

for 10 cars you can expect cars

We can expect 3 cars to get at most 33 mpg.

B) n=10

the probability that the sample mean is at most 33 mpg =

using formula NORM.S.DIST(-2.1082, TRUE)

C)Z score for 30mpg is

30mpg is 1.67 standard deviation below the mean which is not unusual.

Score that are more than 2 standard deviations away from the mean can be considered unusual.

the probability that we get a score 30 is

Probability of getting this score is greater than 3% which is not unusual