SOLUTION: Please show me how to solve this problem, thank you! The average age of a vehicle registered in Canada is about 100 months and the standard deviation for the population is 19..

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Question 1203243: Please show me how to solve this problem, thank you!
The average age of a vehicle registered in Canada is about 100 months and the standard deviation for the population is 19..
If a random sample of 33 vehicles is selected, find the probability (as percent) that the mean of their age is between 105 and 107 months.
The probability is: %
(Round your answer to the nearest whole percent)
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
mean of population is 100 months.
standard deviation of population is 19.
sample size is 33
since you are looking for the mean of the sample, use the standard error rather than the standard devition.
standard error = standard deviation / square root of sample size = 19 / sqrt(33) = 3.3075.
you want to know the probability that the mean age is between 105 and 107 months.
since you have the standard deviastion of the population, use the z-score.
that formula is z = (x-m)/s
z is the z-score
x is the sample mean
m is the popultion mean.
s is the standard error.
for x = 105, the formula becomes z = (105 - 100) / 3.3075 = 1.626.
for x = 107, the formula becomes z = (107 - 100) / 3.3075 = 2.276.
the area to the left of z = 1.626 = .9480
the area to the left of z = 2.276 = .9886
the area in between is the larger area minus the smaller area = .0406.
that's the probability of getting a z-score between 1.6726 and 2.276.
that is also the probability of getting an average age between 105 and 107.

using the z-score calculator at https://davidmlane.com/hyperstat/z_table.html, this is what the output looks like.

you could use the z-score tables, but the use of the calculator is easier and allows for greater accuracy.