1)

Assume that a sample is used to estimate a population mean ??.Find the 99.9% confidence interval for a sample of size 585 with amean of 74.4 and a standard deviation of 16.6. Enter your answersaccurate to four decimal places.

Confidence Interval:

2) You measure 20 textbooks' weights, and find they have a meanweight of 74 ounces. Assume the population standard deviation is10.9 ounces. Based on this, construct a 95% confidence interval forthe true population mean textbook weight.

Keep 4 decimal places of accuracy in any calculations you do.Report your answers to four decimal places.

Confidence Interval:

3)

A population of values has a normal distribution with?=146.5?=146.5 and ?=53.4?=53.4. You intend to draw a random sampleof size n=114n=114.

Find the probability that a single randomly selected value isless than 141.
P(X < 141) =

Find the probability that a sample of size n=114n=114 israndomly selected with a mean less than 141.
P(¯xx¯ < 141) =  Enter your answers asnumbers accurate to 4 decimal places.

4)

CNNBC recently reported that the mean annual cost of autoinsurance is 987 dollars. Assume the standard deviation is 257dollars. You take a simple random sample of 94 auto insurancepolicies.

Find the probability that a single randomly selected value is lessthan 968 dollars.
P(X < 968) =

Find the probability that a sample of size n=94n=94 is randomlyselected with a mean less than 968 dollars.
P(¯xx¯ < 968) =

Enter your answers as numbers accurate to 4 decimal places.