HARDMAN MAT 2170 Exam #3 Review Sheet

| June 14, 2018

HARDMANMAT 2170Exam #3 Review Sheet1. Know the definitions of the following terms:CensusStandard ErrorUniform Continuous DistributionStatisticSampleNormal DistributionPoint EstimatorSampling DistributionParameterCentral Limit TheoremZ-numberSampling FrameSimple Random SampleStratified Random Sampling2Cluster SamplingSystematic SamplingConvenience SamplingJudgment Sampling2. The mean hourly pay rate for financial managers in the East North Central region is$32.62, and the standard deviation is $2.32. Assume that pay rates are normallydistributed. What hourly rate separates the top 5% of pay rates from the lower 95%of pay rates for these financial managers?3. Each sample statistic on the left is used as a point estimator of one of the populationparameters on the right. Match them up correctly. Each letter is used once, or not atall.____X____p____sA.B.C.D.E.p34. A recent survey of MBA graduates revealed that their mean salary was $95,000, witha standard deviation of $12,000. If a simple random sample of 50 MBA graduates isto be taken:a. What is the probability that the sample mean salary will exceed $98,000?b. What is the probability that the sample mean salary will fall between $92,000 and$96,500?5. Given that z is the standard normal random variable, find z for each situation:a. The area to the right of z is 0.1314.b. The area between z and z is 0.903.6. A population has a mean of 200 and a standard deviation of 50. A simple randomsample of size 100 will be taken and the sample mean will be used to estimate thepopulation mean. Specify the sampling distribution of X .47. If the population proportion is 0.4, and a simple random sample of size 200 will betaken:a. Specify the sampling distribution of p , the sample proportion.b. What is the probability that the sample proportion will take a value between 0.36and 0.42?8. Given that z is the standard normal random variable, sketch the appropriate figure thataccompanies each probability (complete with the appropriate shading to represent theprobability), and compute the following probabilities:a. P[ Z 1.72]b. P[0.52 Z 2.31]c. P[ Z 0.48]59. The label on a bottle of salad dressing shows the contents to be 16 ounces per bottle.The production operation fills the bottles uniformly according to the followingprobability density function:5, for 15.85 x 16.050, elsewheref ( x)a. Sketch a graph of the pdf.b. What is the probability that the bottle will be filled with between 15.9 and 16.1ounces?c. Calculate the probability that a randomly chosen bottle will be filled with exactly16 ounces.d. Quality control accepts a bottle that is filled to within 0.03 ounces of the numberof ounces shown on the label.What is the probability that a bottle of this saladdressing will fail to meet thequality control standard?

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