5) The lifetime of a medical device s a normally distributed rv with standard

deviation of 2 years. An experiment is conducted to test 15 medical devices
and find their lifetimes to be:
a. If the population mean is known to be 15 years, what is the probability
that the mean lifetime of these 15 devices is 10 years
b. In a) what is the probability that the mean lifetime is more than 5
years
c. If the population mean is not known, and the obtained lifetimes are:2,
3, 5, 7, 7, 4, 1, 10, 13, 14, 15, 14, 17, 19, 20. Find the 90% confidence
interval for the population mean
d. Repeat c) for the case when the population standard deviation is not
known

a. Z = (score-mean)/SEm

SEm = SD/√n

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to your Z score.

b. Same.

c. 95% = mean ± 1.645 SEm

d. I don't know how to do that.