1.) A simple random sample of 22 observations is derived from a normally distributed population with a known standard deviation of 5.4.[You may find it useful to reference thez table.] a.Is the condition thatXXis normally distributed satisfied? multiple choice 1

• Yes
• No

b.Compute the margin of error with 99% confidence.(Round intermediate calculations toat least 4 decimal places. Round "z" value to 3 decimal places and final answer to 2 decimal places.)

Margin of error

c.Compute the margin of error with 95% confidence.(Round intermediate calculations toat least 4 decimal places. Round "z" value to 3 decimal places and final answer to 2 decimal places.

Margin of error d.Which of the two margins of error will lead to a wider interval? multiple choice 2

• The margin of error with 95% confidence.
• The margin of error with 99% confidence.

2.) In order to estimate the mean 30-year fixed mortgage rate for a home loan in the United States, a random sample of 30 recent loans is taken. The average calculated from this sample is 6.15%. It can be assumed that 30-year fixed mortgage rates are normally distributed with a standard deviation of 0.4%. Compute 90% and 95% confidence intervals for the population mean 30-year fixed mortgage rate.(You may find it useful to reference thez table.Round intermediate calculations to at least 4 decimal places. Round "z" value to 3 decimal places and final answers to 2 decimal places. Enter your answers as percentages, not decimals.)

Confidence level	Confidence interval	Confidence interval
90%	%	To %
95%	%	To %

3.) A family is relocating from St. Louis, Missouri, to California. Due to an increasing inventory of houses in St. Louis, it is taking longer than before to sell a house. The wife is concerned and wants to know when it is optimal to put their house on the market. Her realtor friend informs them that the last 24 houses that sold in their neighborhood took an average time of 150 days to sell. The realtor also tells them that based on her prior experience, the population standard deviation is 65 days. [You may find it useful to reference the z table.]

a. What assumption regarding the population is necessary for making an interval estimate for the population mean?

• Assume that the central limit theorem applies.
• Assume that the population has a normal distribution.

b. Construct the 99% confidence interval for the mean sale time for all homes in the neighborhood. (Round intermediate calculations to at least 4 decimal places. Round "z" value to 3 decimal places and final answers to 2 decimal places.)

Confidence interval _____to______