A fitness center is interested in finding a 90% confidence interval for the mean number of days per week that Americans who are members of a fitness club go to their fitness center. Records of 270 members were looked at and their mean number of visits per week was 2.5 and the standard deviation was 2.9. Round answers to 3 decimal places where possible. a. To compute the confidence interval use a ? distribution. b. With 90% confidence the population mean number of visits per week is between and visits. c. If many groups of 270 randomly selected members are studied, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean number of visits per week and about percent will not contain the true population mean number of visits per week.

c. What is the likelihood of selecting a sample with a mean of at least $139,000? Note: Round your value to 2 decimal places and final answer to 4 decimal places. Probability d. What is the likelihood of selecting a sample with a mean of more than $127,000? Note: Round your value to 2 decimal places and final answer to 4 decimal places. Probability e. Find the likelihood of selecting a sample with a mean of more than $127,000 but less than $139,000. Note: Round your z-value to 2 decimal places and final answer to 4 decimal places

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To the Internal Revenue Service (IRS), the reasonableness of total itemized deductions depends on the taxpayer's adjusted gross income. Large deductions, which include charity and medical deductions, are more reasonable for taxpayers with larg given level of income, the chances of an IRS audit are increased. Data (in thousands of dollars) on adjusted gross income and the average or reasonable amount of itemized deductions follow. Adjusted Gross Income Itemized Deductions ($1,000s) 22 ($1,000) 9.6 27 9.6 32 10.1 48 11.1 65 13.5 85 120 15.7 25.5 (a) Develop a scatter diagram for these data with adjusted gross income as the independent variable. 30 25 20 15 10 5 30 25 20 15 10 5+ 30 25- 20- 15- 10- .. 5- 0 20 40 60 80 100 120 140 Adjusted Gross Income ($1,000s) 0 20 40 60 80 100 120 140 0 Adjusted Gross Income ($1,000s) 20 40 60 80 100 120 140 Adjusted Gross Income ($1,000s) 30 25 20 15 10 5- 0 20 40 60 80 100 Adjusted Gross Income ($1,000s) 120 140 G (b) Use the least squares method to…

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