ASK YOUR TEACHER Quick Start Company makes 12-volt car batteries. After many years of product tutingr the company knows that the average life of a Quick Start battery is normain distributed, with a mean of 43.2 15. [-12 Points] months and a standard deviation of 3.5 months. I USE SALT (a) If Quick Start gualantea a full refund on any battery that falls within the 36-month period after purchase, what percentage of its batteries will the company expect to replace? (Round your answer to two decimal places.) % (b) If Quick Start does not wantto make refunds for more than 10% of its batteriu under the full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)? months Need Help? ASK YOUR TEACHER At Burnt Mesa Pueblo, archaeological studies have used the method of tree-ring dating in an effort to determine when prehistoric people lived In the pueblo. Wood from several excavations gave a mean of (year) 1254 with a standard deviation of 29 years. The distribution of dates was more or less mound-shaped and symmetric about the mean. Use the empirical rule to estimate the 16. [-13 Points] following. (a) a range of years centered about the mean in which about 68% of the data (tree-ring dates) will be found between and AD. (b) a range of years centered about the mean in which about 95% of the data (tree-ring dates) will be found between and AD. (c) a range of years centered about the mean in which almost all the data (tree-ring dates) will be found between and AD. 17. [-/5 Points] DETAILS Calcululate relative frequency and cumulative frequency. Round relative frequency to two decimal places. X f Relative Cumulative Frequency Frequency 5 6 4 7 3 9 2 2 1 318. [-/6 Points] DETAILS For this problem, carry at least four digits after the decimal in your calculations. In a random sample of 60 professional actors, it was found that 39 were extroverts. LO USE SALT (a) Let p represent the proportion of all actors who are extroverts. Find point estimates for p and q. (Round your answer to four decimal places.) P = (b) Find a 90% confidence interval for p. Find the maximal margin of error. (Round your answer to two decimal places.) E = Report the bounds from the 90% confidence interval for p. (Round your answers to two decimal places.) lower limit upper limit Give a brief interpretation of the meaning of the confidence interval you have found. O We are 90% confident that the true proportion of actors who are extroverts falls outside this interval. We are 10% confident that the true proportion of actors who are extroverts falls within this interval. We are 90% confident that the true proportion of actors who are extroverts falls within this interval. We are 10% confident that the true proportion of actors who are extroverts falls above this interval.19. [-/2 Points] DETAILS MY NOT Find z such that 84% of the standard normal curve lies to the left of z. (Round your answer to two decimal places.) LA USE SALT Z = Sketch the area described. C 0 Z C Z 0 C 0 Z Z 020. [-/3 Points] DETAILS MY NOTES ASK YOUR TEACHER The qualified applicant pool for five management trainee positions consists of seven women and six men. (a) How many different groups of applicants can be selected for the positions? (b) How many different groups of trainees would consist entirely of women? (c) Probability extension: If the applicants are equally qualified and the trainee positions are selected by drawing the names at random so that all groups of five are equally likely, what is the probability that the trainee class will consist entirely of women? (Round your answer to four decimal places.) Need Help? Read It Watch It21. [-/4 Points] DETAILS MY NOTES ASK YOUR TEACHER A research team conducted a study showing that approximately 25% of all businessmen who wear ties wear them so tightly that they actually reduce blood flow to the brain, diminishing cerebral functions. At a board meeting of 15 businessmen, all of whom wear ties, what are the following probabilities? (Round your answers to three decimal places.) LA USE SALT (a) at least one tie is too tight (b) more than two ties are too tight (c) no tie is too tight (d) at least 13 ties are not too tight Need Help? Read It 22. [-/4 Points] DETAILS MY NOTES ASK YOUR TEACHER What price do farmers get for their watermelon crops? In the third week of July, a random sample of 42 farming regions gave a sample mean of x = $6.28 per 100 pounds of watermelon. Assume that o is known to be $2.00 per 100 pounds. (a) Find a 89% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop. What is the margin of error? (Round your answers to two decimal places.) lower limit $ upper limit margin of error (b) Find the minimal sample size necessary for a 89% confidence level with maximal error of estimate E = 0.43 for the mean price per 100 pounds of watermelon. (Round your answer to a whole number.) farming regions23. [-/15 Points] DETAILS MY NOTES ASK YOUR TEACHER The U.S. Department of Transportation, National Highway Traffic Safety Administration, reported that 77% of all fatally injured automobile drivers were intoxicated. A random sample of 52 records of automobile driver fatalities in a certain county showed that 33 involved an intoxicated driver. Do these data indicate that the population proportion of driver fatalities related to alcohol is less than 77% in Kit Carson County? Use a = 0.05. LA USE SALT (a) What is the level of significance? State the null hypothesis Ho and the alternate hypothesis H1. Ho: P ---Select--- H: p ---Select--- (b) What sampling distribution will you use? The Student's t The standard normal since np ---Select--- ---Select---C and nq ---Select--- E ---Select--- What is the value of the sample test statistic? (Round your answer to two decimal places.) (c) Find the P-value of the test statistic. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value.O-3 -2 -1 0 1 2 3 -2 -1 0 1 2 3 -2 -1 0 1 2 3 1 -3 -2 0 2 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a? O At the a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the a = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (e) Interpret your conclusion in the context of the application. There is sufficient evidence at the 0.05 level to conclude that the true proportion of driver fatalities related to alcohol in the county is less than 77%. There is insufficient evidence at the 0.05 level to conclude that the true proportion of driver fatalities related to alcohol in the county is less than 77%.25. [-/4 Points] DETAILS MY NOTES ASK YOUR TEACHER The incubation time for a breed of chicks is normally distributed with a mean of 21 days and standard deviation of approximately 2 days. Look at the figure below and answer the following questions. If 892 eggs are being incubated, how many chicks do we expect will hatch in the following time periods? Round your answers to whole numbers. (Note: In this problem, let us agree to think of a single day or a succession of days as a continuous interval of time. Assume all eggs eventually hatch.) Area Under a Normal Curve 2.35% 13.5% 34% 34% 13.5% 2.35% 1 - 30 1 - 20 4- 0 LL uto u+ 20 u+ 30 68% 959 99.7% (a) in 15 to 27 days chicks (b) in 21 days or more chicks (c) in 19 to 23 days chicks (d) in 17 to 25 days chicks26. [-/1 Points] DETAILS MY NOTES ASK YOUR TEACHER There are three nursing positions to be filled at Lilly Hospital. Position 1 is the day nursing supervisor; position 2 is the night nursing supervisor; and position 3 is the nursing coordinator position. There are 15 candidates qualified for all three of the positions. Determine the number of different ways the positions can be filled by these applicants. Need Help? Read It Watch It Master It