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? (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 evident 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. Assuming 40% of all people who visit doctors have problems of a psychosomatic nature, the probability of observing less than or equal to 4 people with psychosomatic problems in a sample of 25 people is greater than 0.05. Hence, this is not an unlikely event and we have no reason to doubt the psychiatrist's theory. Assuming 40% of all people who visit doctors have problems of a psychosomatic nature, the probability of observing less than or equal to 4 people with psychosomatic problems in a sample of 25 people is greater than 0.05. Hence, this is an unlikely event and we should begin to question the psychiatrist's theory.Assuming 40% of all people who visit doctors have problems of a psychosomatic nature, the probability of observing less than or equal to 4 people with psychosomatic problems in a sample of 25 people is less than 0.05. Hence, this is not an unlikely event and we have no reason to doubt the psychiatrist's theory. Assuming 40% of all people who visit doctors have problems of a psychosomatic nature, the probability of observing less than or equal to 4 people with psychosomatic problems in a sample of 25 people is less than 0.05. Hence, this is an unlikely event and we should begin to question the psychiatrist's theory. You may need to use the appropriate appendix table or technology to answer this question.
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. (Round your answer to two decimal places.) (d) Do these data disagree with the forecast of a "20% probability of rain"? Explain. The observed event is more than 2 standard deviations above the mean, so it is unlikely assuming p is accurate. The observed event is more than 2 standard deviations above the mean, so it is not unlikely assuming p is accurate.The observed event is less than 2 standard deviations above the mean, so it is not unlikely assuming p is accurate. The observed event is less than 2 standard deviations above the mean, so it is very unlikely assuming p is accurate.
6. The alleles for black (B) and white (b) feather color in chickens show incomplete dominance; individuals with the gene pair Bb have "blue" feathers. When one individual that is homozygous dominant (BB) for this trait is mated with an individual that is homozygous recessive (bb) for this trait, 1/2 will carry the gene pair Bb. Let x be the number of chicks with "blue" feathers in a sample of n = 25 chicks resulting from this type of cross. (a) Does the random variable x have a binomial distribution? If not, why not? If so, what are the values of n and p? Yes, x has a binomial distribution with n = 2 and p = 0.25. Yes, x has a binomial distribution with n = 25 and p = 0.25.Yes, x has a binomial distribution with n = 25 and p = 0.5. No, x does not have a binomial distribution because the probabilities of having "blue" feathers is not the same as the probabilities of having black or white feathers. No, x does not have a binomial distribution because the trials are not independent. (b) What is the mean number of chicks with "blue" feathers in the sample? (c) What is the probability of observing fewer than eight chicks with "blue" feathers? (Round your answer to three decimal places.) (d) What is the probability that the number of chicks with "blue" feathers is greater than or equal to 13 but less than or equal to 16? (Round your answer to three decimal places.) You may need to use the appropriate appendix table to answer this question.
7. A West Coast university has found that about 90% of its accepted applicants for enrollment in the freshman class will actually enroll. In 2020, 1,287 applicants were accepted to the university. Within what limits would you expect to find the size of the freshman class at this university in the fall of 2020? (Round your answers to the nearest whole number.) lower limit freshmen upper limit freshmen
8. How do you survive when there's no time to eatfast food, no food, a protein bar, candy? A USA Today snapshot indicates that 36% of women aged 25-55 say that, when they are too busy to eat, they get fast food from a drive-thru. A random sample of 100 women aged 25-55 is selected.
9. A bar chart labeled "How Women Eat on the Run" has 4 bars along the horizontal axis. The vertical axis has values from 0% to approximately 42%. The labels and approximate heights of the bars are as follows.

• Drive-Thru: 36%
• Skip a Meal: 35%
• Protein Bar or Shake: 15%
• Candy/Snack Food: 14%
• (a) What is the average number of women who say they eat fast food when they're too busy to eat?
• (b) What is the standard deviation for the number of women who say they eat fast food when they're too busy to eat?
• (c) If 50 of the women in the sample said they eat fast food when they're too busy to eat, would this be an unusual occurrence? Explain. Since the z-score corresponding to x = 50 is between 1 and 0, it is not unusual. Since the z-score corresponding to x = 50 is between 0 and 1, it is not unusual.Since the z-score corresponding to x = 50 is between 1 and 2, it is not unusual. Since the z-score corresponding to x = 50 is between 2 and 3, it is somewhat unusual. Since the z-score corresponding to x = 50 is greater than 3, it is very unusual.

1. Fifty percent of all Americans who travel by car look for gas stations and food outlets that are close to or visible from the highway. Suppose a random sample of n = 25. Americans who travel by car are asked how they determine where to stop for food and gas. Let x be the number in the sample who respond that they look for gas stations and food outlets that are close to or visible from the highway. (a) What are the mean and variance of x? (b) Calculate the interval ? 2?. What values of the binomial random variable x fall into this interval? (Enter your answers as a comma-separated list.) (c) Find P(8 x 17). How does this compare with the fraction in the interval ? 2?for any distribution? For mound-shaped distributions? This value with Tchebysheff's Theorem which states that at least _______% of the measurements should be in this interval. The value the Empirical Rule which states that approximately _________% of the measurements should be in this interval. You may need to use the appropriate appendix table to answer this question.