Question

Problem 05 Empirical Rule : Several years of final exam scores in statistics courses for a local university are normally distributed with a mean of 81 and a standard deviation of 8. If the lowest 2.5% of the scores on this test qualifies for a failing grade (F), use the empirical rule to calculate the score a student would need on this test to pass the final exam? show your work integer answer

Problem 08 Expected Value and Life Insurance Payouts : There is a 0.9985 probability that a randomly selected 60-year-old female lives through the year U.S. Department of Health and Human Services. A Fidelity life insurance company charges $180 for insuring that the female will live through the year. If the female does not survive the year, the policy pays out $100,000 as a death benefit.

1. From the perspective of the 60-year-old female, what are the monetary values corresponding to the two events of surviving the year and not surviving?

2. If a 60-year-old female purchases the policy, what is her expected value?

3. Can the insurance company expect to make a profit from many such policies? Why?

Problem 11 Continuous Random Variables: Empirical Rule:  Scores on an examination are assumed to be normally distributed with mean 78 and variance 10. Suppose that students scoring in the top 10% of this distribution are to receive an A grade. If you are asked “What is the minimum score a student must achieve to earn an A grade?”, can you use the empirical rule to answer this question? Explain your answer.

Answer 1