# STAT 500 STAT500 Homework 3 Solution (Penn State University)

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STAT 500 STAT500 Homework 3 Answers (Penn State University)

1. Are you someone who prefers to take risk or avoid risk?

2. A professor always assigns final grades such that 20% are A, 40% are B, 30% are C, 5% are D, and 5% are F. The grade point scores are 4 for A; 3 for B; 2 for C; 1 for D; and 0 for F.

3. From a recent General Social Survey response to question, “What is the ideal number of children for a family to have?” The probability distribution of X equal to the response is approximated by the following table according to the sex of the person responding:

4. Imagine a company with a large number of employees (e.g. over a thousand) from which it can choose someone for management training. Furthermore, half of these available employees are female. Since the management training program began, 10 employees have been selected and all were male. What is the probability that out of 10 selected 0 would be female if there was no gender bias in the selection process?

5. Assume each newborn baby has an approximate probability of 0.51 of being male. For a family of four children Let X = number of children that are females.

6. A marketer uses random digit dialing to call people and try to interest them in donating to a national charitable organization. From past experience, she is successful on 2% of her calls. In a typical work day she makes 200 calls. Let X represent the number of calls on which she is successful. D

7. A World Health Organization study of health in various countries reported that in Canada, the systolic blood pressure readings (i.e. this is the top number of your blood pressure e.g. the ‘120’ if your bp is 120/84) have a mean of 121 and a standard deviation of 16. A reading above 140 is considered to be high blood pressure. Assuming these readings are approximately normal, answer the following.

8. Using a college cost estimator, the average of campus rental at Penn State is approximately \$547 per month. Suppose these rates are roughly normal with a standard deviation of \$100. What proportion of rentals:

9. Two popular standardized tests use in the undergraduate admission process are the SAT and the ACT. For the math portion of each test, the SAT has (μ = 500 and σ = 100) while for the ACT these are (μ = 21 and σ = 4.7). Both metrics have score distributions that are approximately normal. Which score is relatively higher, and SAT score of 600 or an ACT score 0f 25? Explain.

10. Refer back to question 8. Say you take a random sample of 25 students living off campus.

11. According to the Alzheimer’s Association, Alzheimer’s disease affects 1 in 10 people over the age of 65. A study was conducted on health issues facing by people over the age of 65. What would be the shape, mean and standard error of the sampling distribution of the proportion who suffer from Alzheimer’s disease if the sample size is 200 and if it were 800?

12. Referring back to problem 11, if the sample size were 200 what is the probability that the sample proportion would be at least 12.5%? Does this outcome seem likely? Explain.

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