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1. Assume the following data were gathered by a manufacturer

by | Jul 25, 2022 | Recent Orders

1. Assume the following data were gathered by a manufacturer of a robotics component, inunits of days of continuous use until the component fails. There are 60measurements in this data set. Show a histogram of this data set with 10 binsof equal size, spanning the range from the data minimum to the data maximum.142, 147, 127, 161, 145, 137, 122, 123, 141, 139, 139135, 135, 130, 147, 118, 154, 133, 136, 129, 139, 131143, 130, 160, 127, 127, 145, 144, 155, 128, 124,144133, 136, 133, 151, 131, 133, 119, 122, 139, 128, 121142, 136, 148, 136, 121, 131, 125, 120, 123, 145, 140150, 136, 135, 133, 1342. A university has been tracking the percentage of alumni giving to its annual fundeach year for the past 10 years. The data is given here.14%, 13%, 15%, 21%, 19%, 24%, 25%, 28%, 25%. 31%Answer the following questions about this data.a.what are its mean and median?b.What is the procedure for using mean and median to determine whether the datais skewed, and if so, in what direction?c.Apply the procedure you described to the mean and median computed in part a.3. Assume you have a data set from a normally distributed random variable. Answer thefollowing questions about it.a.Will the random variable be discrete, continuous, or neither? How do youknow?b. Will the data be qualitative or quantitative? How do you know?4. A nurse is considering going back to graduate school to earn a Ph.D. inbiochemistry. One of the schools she visits tells her that the average time toearn the degree she’s considering is 5.5 years. Show that this statement is notsufficiently precise by giving two different explanations of what it mightmean.5. Under which of the following conditions would it be appropriate to use a Binomialrandom variable? In each case, explain why your answer is correct.a. A department will interview 10 candidates for a position, and call back forsecond interviews those who answer the interview questions to the satisfactionof all the interviewers. They hope to call back at least 3, but past experiencesuggests an average of about 1 call back per 4 interviews.b. A factory posts on the wall the number of days since its last safetyinfraction of injury. In the past year, the factory has had a safety infractionor injury on 6 different days. The factory is interested in the n umber of daysthat can be expected to elapse without an injury.c. Fifteen of a doctor’s patients have the same ailment. Studies have shownthat about 86.5% of patients with this ailment respond to a certain drug. Thedoctor prescribes the drug to all 15, but the number who will respond in thiscase is, of course, not known in advance.6. The mean time for a racecar driver’s crew to perform a pit stop is 13.2 seconds,with a standard deviation of 0.9 seconds. To maintain his current lead, thedriver needs a pit stop in 12.5 seconds or less. Assuming this random variableis normally distributed, what is the probability of the driver getting the pitstop in a short enough time to maintain is lead?7. From a sample of size 175, the sample mean is x bar=54.37 and sample standarddeviation is s= 7.07.a. Construct a 95% confidence interval for the population mean and show yourwork.b. Explain how your work in part a would have been different if the sample sizehad been only 12 instead.8. A random sample from the population of registered voters in California is to betaken and then surveyed about an upcoming election. What sample size should beused to guarantee a sampling error of 3% or less when estimating p at the95%confidence level?

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