Question

Suppose that we wanted to use a random sample to determine the average income in the country. If we know the population standard deviation is 11,933, how large does our sample need to be to get a standard error of 99? If you end up with something that isn’t a whole number, that is ok, just round to four decimal places anyway.

The average clothes washer uses 15 gallons of water per load, with a standard deviation of 3.0 gallons. What is the probability that a random sample of 90 loads will provide a sample mean within one half gallon of the population mean?

Answer 1

1) Given that, population standard deviation = 11933

standard error = 99

We want to find the sample size (n),

Therefore, required sample size is 14529

2) Given that, mean = 15 gallons and

standard deviation = 3.0 gallons

sample size (n) = 90

We want to find,

Therefore, required probability is 0.8858