stats question

Question

The average age of a vehicle registered in Canada is about 97 months. If a random sample of 47 vehicles is selected, find the probability that the mean of their age is between 100 and 103 months. Assume the standard deviation for the population is 20.

 

 

 

 

 

 

 

I am using normcdf(100,103,97,20) but that isn't the right answer

Answer 1

mean 97

sd = 20

n = 47

what percent are between 100 and 103??

find z scores and corresponding areas under the normal curve using z tables. then subtract

z1 = (100-97)/20/sqr47 = 3sqr47/20 = .15sqr47 = about .1028

z2 = 2z1 = (103-97)/20/sqr47 = .3sqr47 = about .2057

area given z1 = about .041

area given z2 = about .081

area2 minus area1 = about 4%