13. Assume that gas mileage for cars is normally distributed with a mean of 23.5 miles per gallon and a standard deviation of 10 miles per gallon. Show all work. Just the answer, without supporting work, will receive no credit.
(a) What is the probability that a randomly selected car gets between 15 and 30 miles per gallon? (Round the answer to 4 decimal places)
(b) Find the 75th percentile of the gas mileage distribution. (Round the answer to 2 decimal places)
14. Based on the performance of all individuals who tested between 2015 and 2017, the GMAT total scores are normally distributed with a mean of 561.27 and a standard deviation of 119.31. (https://www.gmac.com/gmat-other-assessments/accessing-gmat-exam-scores-and-reports/gmat- scoring-by-exam-section-normal-view#tab5). Show all work. Just the answer, without supporting work, will receive no credit.
(a) For a sample of size 100, state the standard deviation of the sample mean (the “standard error of the mean”). (Round your answer to three decimal places)
(b) Suppose a sample of size 100 is taken. Find the probability that the sample mean GMAT total scores is more than 575. (Round your answer to three decimal places)
15. A survey showed that 980 of the 1500 adult respondents believe in global warming.
(a) Construct a 99% confidence interv al estimate of the proportion of adults believing in global warming. (Round the lower bound and upper bound of the confidence interval to three decimal places) Include description of how confidence interval was constructed.
(b) Describe the results of the survey in everyday language.