STA 6166 – Exam 1 – Spring 2016 PRINT Name _________________________Q.1. Chicago food establishments are classified by 3 levels of Risk (High, Medium, and Low). The proportions (probabilities) are: P(High) = .65, P(Medium) = .22, P(Low) = .13. The probabilities of Failing inspection are .21 among High risk, .23 among Medium Risk, and .33 among Low Risk.p.1.a. Compute the probability a randomly selected establishment Fails inspection.p.1.b. Compute the probability of each risk type, given the establishment fails inspection..P(High Risk | Fail) = __________ P(Medium Risk | Fail) = _________ P(Low Risk | Fail) = __________Q.2. The June monthly rainfall totals (in inches) for a sample of 5 Orlando years were: 10, 5, 5, 6, 9. Give the sample mean, median, and standard deviation of the monthly rainfall totals (show all work).Mean = _______________ Median = _________________ Std. Deviation = __________________Q.3. An examination is given with n = 5 multiple-choice questions, each with 4 choices, and 1 correct answer. Astudent arrives for the exam completely unprepared, and will randomly guess on each question.p.3.a. What is the probability the student will get at least 1 correct.p.3.b. What are the mean and standard deviation of the number correct answers if this exam was given many times to people randomly guessing answers? Q.4. Elite female hammer thrower Anita Włodarczyk has a competitive mean distance thrown of 73.36 meters and standard deviation of 2.74 meters. Translate her mean and standard deviation to feet. (1 foot = 0.3048 meters).Q.5. An engineer is interested in estimating the population mean lifetime of a new type of light bulb. Based on a pilotstudy, they estimate the standard deviation to be 100 hours. How large of a sample will be needed to have a margin oferror of 10 hours with 95% confidence?Q.6. A random sample of n = 16 female runners at the Washington, DC marathon had a sample mean speed of 6.04 milesper hour with a sample standard deviation of 0.78 miles per hour.p.6.a. Compute the estimated standard error of the sample mean.p.6.b. Give the degrees of freedom corresponding to the answer in p.6.a.p.6.c. Obtain a 95% confidence interval for (the population mean of all female runners in that marathon).Q.7. A researcher wishes to test whether the population mean time for her factory’s workers to complete a task exceeds 30minutes. She takes a random sample of 64 workers from her firm’s large factory, and measures the time it takes eachworker to complete the task.p.7.a. Give the null and alternative hypothesesp.7.b. The sample mean was 36 minutes and the sample standard deviation was 24 minutes. Compute the test statistic.p.7.c. Obtain the p-value, based on the z-distribution.Q.8. Body Mass Indices (BMI) for English Premier League (EPL) football players are approximately normally distributedwith a mean of 23.00 and standard deviation of 1.70. p.8.a. What is the probability a randomly selected EPL player has a BMI above 24.5?p.8.b. Between what 2 BMI levels do the middle 50% of all EPL players fall?p.8.c. What is the sampling distribution of sample means of sample size = 16 from this population? Give the distributionsymbolically and draw a graph of
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