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The cоntent оf the exаm is belоw. You mаy downloаd the exam as a pdf here. You must not share this file with anyone in the class. Especially while the exam is open. You may not post this exam anywhere else even after the class is completed. (12 points) Suppose the chance of a meteor hitting your hometown on any given day is 1 in 5 million. What is the chance that your town avoids a meteor strike for the next 18 years? Assume 365 days per year, and strikes are independent day to day. (12 points) A delivery company is testing a new routing algorithm. Historically, 98% of packages are delivered on time. A quality control analyst selects 50 random deliveries under the new algorithm. Confirm that this experiment satisfies the criteria for a Binomial Probability Experiment. Calculate the mean and standard deviation of the number of on-time deliveries. Would it be unusual for only 45 packages to arrive on time? (15 points) A tech company finds that the battery life of its new laptop model is normally distributed with a mean of 9 hours and a standard deviation of 1.2 hours. What proportion of laptops last between 8 and 10.75 hours on a full charge? The company claims “most laptops will last at least 7.5 hours.” What proportion of batteries fail to meet this claim? The company would like to include the phrase “Lasts up to hours” in its advertising, using the cutoff battery life for the top 5% of tested laptops. (12 points) Daily water consumption per household in a city is strongly right-skewed with a mean of 205 gallons and a standard deviation of 130 gallons. A utility company samples 507 homes. Determine the sampling distribution for the mean water consumption. What is the probability that the mean daily water use is between 195 and 215 gallons? (12 points) In one study it was found that 92% of all homes have a functional smoke detector. Suppose this proportion is valid for all homes. Suppose we select a random sample of 650 homes. Find the sampling distribution for the proportion of homes in our sample that have a functional smoke detector. Assume the population distribution is the same as in the study. Find the probability that between 90.3% and 94.4% of the homes in the sample will have a functional smoke detector. (16 points) In a certain region, regulations require that labels on prepackaged products must be reasonably accurate. If you want to label a can of soda as having 500 ml then at least 90% of the cans sold must have at least 490 ml of soda.We would like to estimate the proportion of cans of our soda brand that satisfy the volume requirement. In a random sample of 570 cans, 515 had at least 490 ml of soda. Compute the estimated standard error. Compute the margin of error for a 96% confidence interval. Construct the 96% confidence interval for the proportion. Based on this data, are you confident the cans are filled to regulation? Briefly explain. (15 points) In a study of post-operative recovery times, a sample of 55 patients had an average hospital stay of 4.6 days with a standard deviation of 1.1 days. The hospital constructs a 95% confidence interval for the mean length of stay: (4.30, 4.90) days. The hospital wants to advertise that the average recovery time is under 5 days. Is this supported by the interval? A second researcher uses the same data but constructs a 90% confidence interval. Would this be wider or narrower than the 95% one? The hospital would like to do a similar study with a different sample. They want to keep the confidence level at 95% but make the interval narrower. What do you recommend they do? (12 points) According to a Federal Poverty Measure 12.1% of the U.S. population lives below the poverty line. If the poverty rate of a certain state is above the federal measure, the governor can apply for federal assistance in addressing the problem. In a study, a random sample of 8750 people is surveyed. Of those, 1089 lived below the poverty line. State an appropriate null hypothesis and an appropriate alternative hypothesis for this test. State them both mathematically and verbally. Suppose the poverty rate is actually at the Federal Poverty Measure but the p-value is small enough to reject the null hypothesis. Would this be a Type I or Type II error? The researchers perform the hypothesis test using a 0.1 significance level. They computed a test statistic of 0.9916 with a p-value of 0.16070. Write a brief conclusion to the report to the governor. Use the context of the problem. Copy the following fill in the blank with your name. Below the statement add your signature and today's date.I certify that the work I submit with this exam has been my own, written in my own words, and done according to the rules above. (Signature) (Date)