Have 2 probability problems I am soo lost on, any help would be greatly appreciated, thanks in advance.?

Question

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.

Answer 1

for the first one:
(7.0 - 7.1) / (1.4 / sqrt(7)) = -0.1890.
for the second:

Answer 2

For both of these, compute the z-value:

z = (sample mean - population mean) / (std dev / sqrt(sample size))

then compute the area under the normal curve corresponding to values above this z-value. You can use the link listed below.

For the first one:
z = (7.0 - 7.1) / (1.4 / sqrt(7)) = -0.1890.

The area under the normal curve for z > -0.1890 is 0.575, so there is a 57.5% chance that the sample will have a mean replacement time greater than 7 years.

Answer 3

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