1 The Environmental Protection Agency EPA rates the mean hig

1)      The Environmental Protection Agency (EPA) rates the mean highway gas mileage of the 2011 Ford Edge to be 27 miles per gallon (mpg). Assume the standard deviation is 3 miles per gallon.

a)      If a 2011 Ford Edge is selected at random, find the probability that its gas mileage is

i)        greater than 32 mpg. Would this be considered unusual, and why?

ii)      between 25 and 28 mpg.

b)      Find the miles per gallon that is the 30^th percentile.

c)      Assume a sample of 40 2011 Ford Edges is selected at random. Why can we say the sampling distribution of the mean miles per gallon is approximately normal?

d)     For the sample of 40 2011 Ford Edges selected, find the probability that the mean miles per gallon is less than 28 mpg.

Solution

i (32-27)/3= 1.67

Probablility from normal table is .0475, unusual because less than .05

ii (28-27)/3= .333 prob .6293 (all subsequent probabilities are from the normal table)

25-27/3= -..67 prob .2514

.6293-.2514= .3779 (answer)

b) 30% percentile is -.525= (x-27)/3; x= 25.43

c) Because the sample size is high enough (40) the Central Limit theorem tells us the sampling distribution is normal.

d) (28-27)/3/sqrt(40)= 2.11 prob is .0174