Assignment: (20 points total)
1) In 2019, the average high school GPA for incoming University of Maryland freshman was 4.32 with a standard deviation of 0.285. Suppose UMD freshman are randomly assigned into groups of 25.
For parts b-c, use the normalcdf command in your calculator. To receive credit, write the command and the values you entered. (6 pts)
- a) Find the mean and standard deviation of the sampling distribution and describe the sampling distribution using the notation .
- b) What is the probability of a group having an average high school GPA above 4.5?
- c) What is the probability of a group having an average high school GPA below 4.2?
2) The average age for retirement in the US is heavily skewed left with a mean of 62 years of age and a standard deviation of 5.42 years. (8 pts)
- a) Explain why you cannot determine the probability that a randomly chosen new retiree is older than 62 years of age.
- b) Given a random sample of 5 retirees, can you estimate the probability that the mean retirement age is less than 60? Explain.
- c) Using the notation , describe the sampling distribution of the mean retirement age for random samples of 75 retirees.
- d) What is the probability that the mean retirement age for a sample of 75 retirees is less than 60 years of age? To receive credit, write the command you used and the values you entered.
3) The collapse of the housing bubble in 2008 saw housing prices in the largest cities losing a third of their value, the stock market nearly collapsed, and unemployment doubled. Yet, the story of the recession isn’t necessarily one of loss so much as it is of increasing income inequality. While families hovering around the average net worth lost 36% in the decade spanning from 2003 to 2013, people in the top 95th percentile actually gained 14% in the same tumultuous period. In one large community, a random sample of 55 homes found an average loss in home value of $29, 675 from 2003 to 2013 with a standard deviation of approximately $4,000. (6 pts)
- a) Use the TInterval command in your calculator to find a 98% confidence interval for the mean loss in home value in this community. To receive credit, write the command and the values you entered.
- b) Interpret the interval you found in part (a).
- c) A government official claims that the mean loss is home value is greater than $28,500, does your interval support this claim? Explain.
Solution
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