Sample distributions | Mathematics homework help

A small hair salon in Denver, Colorado, averages about 30 customers on weekdays with a standard deviation of 6. It is safe to assume that the underlying distribution is normal. In an attempt to increase the number of weekday customers, the manager offers a $2 discount on 5 consecutive weekdays. She reports that her strategy has worked since the sample mean of customers during this 5 weekday period jumps to 35. Use Table 1.

a.

What is the probability to get a sample average of 35 or more customers if the manager had not offered the discount? (Round your intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

  Probability

[removed] 

In order to estimate the mean 30-year fixed mortgage rate for a home loan in the United States, a random sample of 28 recent loans is taken. The average calculated from this sample is 5.25%. It can be assumed that 30-year fixed mortgage rates are normally distributed with a standard deviation of 0.50%. Compute a 90% and a 99% confidence interval for the population mean 30-year fixed mortgage rate. Use Table 1. (Round your intermediate calculations to 4 decimal places, “z” value and final answers to 2 decimal places.)

Confidence Level

Confidence Interval             

90%

[removed]to [removed] 

99%

[removed]to ——-

5. 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. They ask their realtor friend for help and she informs them that the last 26 houses that sold in their neighborhood took an average time of 218 days to sell. The realtor also tells them that based on her prior experience, the population standard deviation is 72 days. Use Table 1.

a.

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

b.

Construct a 90% confidence interval of the mean sale time for all homes in the neighborhood. (Round your intermediate calculations to 4 decimal places, “z” value and final answers to 2 decimal places.)

  Confidence interval

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7. The Chartered Financial Analyst (CFA^®) designation is fast becoming a requirement for serious investment professionals. Although it requires a successful completion of three levels of grueling exams, it also entails promising careers with lucrative salaries. A student of finance is curious about the average salary of a CFA^® charterholder. He takes a random sample of 36 recent charterholders and computes a mean salary of $158,000 with a standard deviation of $36,000. Use this sample information to determine the 95% confidence interval of the average salary of a CFA^® charterholder. Use Table 2. (Round your intermediate calculations to 4 decimal places, “t” value to 3 decimal places, and final answers to a whole number.)

  Confidence interval

  [removed] to [removed] 

Executive compensation has risen dramatically beyond the rising levels of an average worker’s wage over the years. Sarah is an MBA student who decides to use her statistical skills to estimate the mean CEO compensation in 2010 for all large companies in the United States. She takes a random sample of six CEO compensations. Use Table 2.

  Firm

Compensation
(in $ millions)

  Intel

8.20

  Coca-Cola

2.76

  Wells Fargo

6.57

  Caterpillar

3.88

  McDonald’s

6.56

  U.S. Bancorp

4.10

a.

How will Sarah use the above information to provide a 90% confidence interval of the mean CEO compensation of all large companies in the United States? (Round your intermediate calculations to 4 decimal places, “sample mean” and “sample standard deviation” to 2 decimal places and “t” value to 3 decimal places, and final answers to 2 decimal places.)

  Confidence interval 

$ [removed]to $ [removed] millions   

9. A survey of 1,026 people asked: “What would you do with an unexpected tax refund?” Forty-seven percent responded that they would pay off debts (Vanity Fair, June 2010). Use Table 1. 

a.

At 95% confidence, what is the margin of error? (Round your intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 3 decimal places.)

  Margin of error

[removed] 

b.

Construct a 95% confidence interval of the population proportion of people who would pay off debts with an unexpected tax refund. (Use rounded margin of error. Round your answers to 3 decimal places.)

  Confidence interval

[removed]to [removed]   

One in five 18-year-old Americans has not graduated from high school (The Wall Street Journal, April 19, 2007). A mayor of a northeastern city comments that its residents do not have the same graduation rate as the rest of the country. An analyst from the Department of Education decides to test the mayor’s claim. In particular, she draws a random sample of 80 18-year-olds in the city and finds that 20 of them have not graduated from high school. Use Table 1.

a.

Compute the point estimate of the proportion of 18-year-olds who have graduated from high school in this city. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

   Point estimate

[removed]  

b.

Use this point estimate to derive a 95% confidence interval of the population proportion. (Round your intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answers to 3 decimal places.)

  Confidence interval

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