Math 2311 EMCF Homework 5 Sections 4.3 - 4.4 Honework will NOT be accepted through email or in person. Homework must be submitted through CourseWare, https://www.casa.uh.edu, before the deadline. Submit this assignment on CourseWare under \"EMCF\" and choose ehw5. 1. True or False: On a statistics exam, Joe's score was at the 20th percentile and John's score was at the 40th percentile, thus, we can say that John's score was twice Joe's. a. True b. False 2. True or False: On the normal curve, the 50th percentile corresponds to the mean. a. True b. False 3. If a distribution has a mean of 48 and standard deviation of 3.2, what is the value that corresponds to a z-score of -1.6? a. b. c. d. e. 38.22 42.88 53.12 46.40 none of these 4. Find P (1.2 < Z < 1.9) a. b. c. d. e. 0.9713 0.8562 0.8020 0.7659 none of these 5. Find c such that P (Z > c) = 0.3859 a. b. c. d. e. -0.29 0.35 -0.35 0.29 none of these 1 0.04 0.00 density 0.08 Use the following to answer questions 6 - 10: The following is the Normal density curve for the MPG of a large sedan with a mean of 26.5 mpg and standard deviation 3.7. 15.4 19.1 22.8 26.5 30.2 33.9 6. What proportion of large sedans have a MPG of less than 25.5 mpg? a. b. c. d. e. 27% 39.35% -39.35% -27% none of these above 7. What is the probability that a sedan has a MPG greater than 30.5 mpg? a. b. c. d. e. 0.86 1.08 0.14 0 none of these above 8. What is the probability that a sedan has between 25.5 and 30.5 mpg? a. b. c. d. e. 0.95 0.2535 0.3935 0 none of these above 2 37.6 9. What is the 90th percentile of the MPG of these sedans? a. b. c. d. e. 23.85 2.65 31.24 0 none of these above 10. Give the first quartile (Q1 )of the MPG of these large sedans. a. b. c. d. e. 6.625 24 29 27.425 none of these above 11. The sampling distributon of a statistic is a. b. c. d. e. The probability that we obtain the statistic in repeated random samples. The mechanism that determines whether randomization was effective. The distribution of values taken by a statistic in all possible samples of the same sample size. The extent to which the sample results differ systematically from the truth. none of these Use the following to answer questions 12 - 13: The high temperature in Chicago for the month of August is approximately normally distributed with mean = 80 F and standard deviation = 8 F. Suppose we take a SRS of 16 days in August and want to determine the sample mean, x high temperature. 12. What is the standard deviation (standard error) of the sample mean high temperature. a. b. c. d. e. 8 2 0.5 10 20 13. What is the probability that a random sample of 16 days in August have a sample mean high temperature of at least 82 F? a. b. c. d. e. 0.5987 0.2500 0.1587 0.8413 Cannot be determined. 3 14. The expected value of the sampling distribution of the sample mean is equal to a. b. c. d. e. the standard deviation of the sampling population the mean of the sampling population the median of the sampling population the population size none of these 15. Power companies kill trees growing near their lines to avoid power failures due to falling limbs in storms. Applying a chemical to slow the growth of the trees is cheaper than trimming, but the chemical kills some of the trees. Suppose that one such chemical would kill 15% of sycamore trees. The power company tests the chemical on 200 sycamores. Consider these a SRS from the population of all sycamore trees. What is the probability that no more than 32 trees are killed? a. b. c. d. e. 0.0571 0.6540 0.3460 0.1598 none of these 4