# Statistics Test #3

I’m trying to study for my Statistics course and I need some help to understand this question.

I have attached the exam below. Please complete it in the indicated time.

Include work and box answers for full credit.Include a rough sketch of any graphs you use. Round your answers to the nearest third decimal place. Write your name on the exam before submitting it.1.(15points) Let Z be the standard normal curve. FindP(Z > 1.28). Interpret this probability in the context of ALL normal curves.2.(15points) According to the National Center for Health Statistics, 22.4% of adults are smokers. A random sample of 250 adults is taken.a.Describe the shape of the sampling distribution of ̂, the sample proportion of adults who smoke. Justify your answer.b.Find the mean and standard deviation of the sampling distribution of ̂.c.In a random sample of 250 adults, what is the probability that at least 60 are smokers?3.(25points) In order to determine the load capacity of a lift, a random sample of 15lifts are stress tested and the maximum weight that each life can bear before malfunctioning is recordedas the “Maximum Load”. Suppose thatthe mean of the maximum load of the 15 selected lifts is1279 pounds and the standard deviation of the maximum loadis 123 pounds.Additionally, it is known that the maximum load of the lifts is normally distributed.a.Verify that the conditions for constructing confidence intervals for the mean are met.b.Compute and interpret a 99% confidence interval for the mean of the maximum weight the lifts can bear.c.Compute and interpret a 99% confidence interval for the standard deviation of the maximum weight the lifts can bear.d.A safety mechanism built into the lift will detect the weight currently on the lift and prevent it from activating if it exceeds a certain threshold. The manufacturers want the mechanism to activate below the maximum weight of nearly all ofthe liftsthey produce. Currently, the mechanism will activate if it detects 1200 pounds or more on the lift. Based off of your answers to parts b and c, should the threshold for the mechanism be changed? Justify your answer.

4.(15points) Residents of a certain large city are going to vote on a bill. A gallop poll surveys 400 registered voters in the city and finds that 224 of them plan on voting “Yes” on the bill.a.Assume the conditions for constructing a confidence interval are met. Compute and interpret a 92% confidence interval for the proportion of voters who plan on voting “Yes” on the bill.b.If at least 50% of voters need to vote “Yes” on the bill in order for it to pass, can we be confident that the bill will pass based on your answer to part a? Justify your answer.

5.(15points) Suppose that a certain consumer advocacy group reports that 72% of the customers of a certain business are “Very satisfied” with the service they received. The group additionally reports a 10% margin of error with a 95% confidence level.a.Interpretthe information provided.b.Suppose the advocacy group wants to reduce the margin of error to 4%. How many individuals should be included in the random sample?

6.(15points) Suppose that it is known that if a certain tablet is fully charged and then left on,the tablet has mean battery life of 145 minutes and the standard deviation of the battery life is 17 minutes. A random sample of 55 tablets is taken.a.Describe the shape of the sampling distribution of ̅, the sample mean of the battery life of the tablet.Justify your answer.b.Find the mean and standard deviation of the sampling distribution of ̅.c.If a random sample of 10 tablets is taken, can we determine the shape of the sampling distribution of ̅?

Extra Credit (5 points):Explain what is meant by a confidence interval having a confidence level of 95%.

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