Quiz 1A

1. Accident records collected by an automobile insurance company give the following information: The probability that an insured driver has an automobile accident is 0.17; if an accident has occurred, the damage to the vehicle amounts to 25% of its market value with probability 0.85, 70% of its market value with probability 0.13, and a total loss with probability 0.07. What premium (in dollars) should the company charge on a $35,000 car so that the expected gain by the company is zero? (Round your answer to the nearest whole number.)
2. If a person is given the choice of an integer from 0 to 9, is it more likely that he or she will choose an integer near the middle of the sequence than one at either end? Twenty-five people are asked to select a number from 0 to 9. Seven of them choose a 4, 5, or 6.(a) If the choice of any one number is as likely as any other, what is the probability of observing seven or more choices of the numbers 4, 5, or 6? (Round your answer to three decimal places.) (b)What conclusions would you draw from the results of part (a)? Observing seven or more people choosing a 4, 5 or 6 an unlikely event, assuming that the integers are all equally likely. Therefore, there is evidence indicating that people are more likely to choose these three numbers than any others. You may need to use the appropriate appendix table to answer this question.
3. A psychiatrist believes that 40% of all people who visit doctors have problems of a psychosomatic nature. She decides to select 25 patients at random to test her theory. (a) Assuming that the psychiatrist's theory is true, what is the expected value of x, the number of the 25 patients who have psychosomatic problems? (b) What is the variance of x, assuming that the theory is true? (c)Find P(x 4).(Use tables and assume that the theory is true. Round your answer to three decimal places.) (d) Based on the probability in part (c), if only 4 of the 25 sampled had psychosomatic problems, what conclusions would you make about the psychiatrist's theory? Explain.
4. College campuses are graying! According to a recent article, one in four college students is aged 30 or older. Assume that the 30% figure is accurate, that your college is representative of colleges at large, and that you sample n = 200 students, recording x, the number of students age 30 or older. (a) What are the mean and standard deviation of x? (Round your standard deviation to three decimal places.) (b) If there are 33 students in your sample who are age 30 or older, would you be willing to assume that the 30% figure is representative of your campus? Explain. (Round your numerical answers to two decimal places.) The observed value, x = 33, lies ____?____ standard deviations below the mean. This observation evidence that the true percentage may not be equal to 30.
5. To check the accuracy of a particular weather forecaster, records were checked only for those days when the forecaster predicted rain "with 20% probability." A check of 20 of those days indicated that it rained on 7 of the 20. (a) If the forecaster is accurate, what is the appropriate value of p, the probability of rain on one of the 20 days? (b) What are the mean ? and standard deviation ? of x, the number of days on which it rained, assuming that the forecaster is accurate? (Round your standard deviation to two decimal places.) (c) Calculate the z-score for the observed value, x = 7. [HINT: Recall that z-score = (x ?)/?.] (Round your answer to 2 decimal places.)