1) The random variable x is normally distributed with mean = 18 and standard deviation = 7.6. Find the following (In each case, draw a sketch).

a) P(x > 20)

b) P(0 < x < 5)

c) Find the value of x that has 88.3% of the distribution's area to its left.

d) Find the value of x that has 64.8% of the distribution's area to its right.

2) The mean amount of money that U.S. adults spend on food in a week is $151 and the standard deviation is $49. Random samples of size 50 are drawn from this population and the mean of each sample is determined. (draw a sketch in b and c)

a) Find the mean and standard deviation of sampling distribution of sample means.

b) What is the probability that the mean amount spent on food in a week for a certain sample is more than $160?

c) What is the probability that the mean amount spent on food in a week for a certain sample is between $135 and $150?

3) In a survey of 2383 U.S. adults, 1073 think that there should be more government regulation of oil companies.

a) Find the point estimate for the population proportion p of U.S. adults who think that there should be more government regulation of oil companies.

b) Construct a 95% confidence interval for the population proportion. Interpret your results.

c) Find the minimum sample size needed to estimate the population proportion at the 99% confidence level when the margin of error is 3%.

4) The data set represents the weights (in grams) of 10 randomly selected adult male fox squirrels from a forest. Assume the weights are normally distributed.

821857782930720821794876810841

a) Find the sample mean and the sample standard deviation (you will need to use sections 3.2 and 3.3 to find the sample mean and the sample standard deviation).

b) Construct a 95% confidence interval for the population mean. Interpret your results.

c) Construct a 99% confidence interval for the population variance.

d) Construct a 99% confidence interval for the population standard deviation.