Replacement times for new Ford Taurus GL automobiles are normally distributed with a mean of 7.1 years and a s

Replacement times for new Ford Taurus GL automobiles are normally distributed with a mean of 7.1 years and a standard deviation of 1.4 years. Find the probability that seven randomly selected Taurus GL automobiles will have a mean replacement time greater than 7.0 years.


Among U.S. households, 24% have telephone answering machines. If a telemarketing campaign involves 2,500 households, find the probability that more than 650 have answering machines.

1-) First you need to find Z-value: (7-7.1)/(1.4/sqrt(7)) = -.1/0.53 = -.189
The prob of having a mean greater than 7 = prob of having a z-value greater than -.189
From the z-table you can find the probability as 57.53%

2-)Same problem, but with proportions. You need to find that prob of proportion greater than 26% (650/2500). You will use t value since the standard deviation is unknown.
T value = (.26-.25)/sqrt((.26*.74)/2500) = 1.14
The prob of having a proportion greater than 26% = prob of having a t-value greater than 1.14 but as n is very large the z-table can be used. From the table you find the prob as 12.71%