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Analysis of Probability Distributions and Statistical Estimations Using Normal and Binomial Distributions

A solved assignment analyzing probability distributions in statistics.

Michael Davis
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Analysis of Probability Distributions and Statistical EstimationsUsing Normal and Binomial Distributions1. Open the Excelfile GolfIncome.xlsx. The data represent income (in thou-sands ofdollars)earned by a population of 40 professionalgolfers from their endorsementdeals. Assume that thedata follow a normal distribution. Using the NORM.DISTand NORM.INV functions, determinethe following:(a) What is the probability that a golfer earned more than 3, 000 thousand dollars?The required probability = 0.6873(b) Whatistheprobabilitythatagolferearnedbetween4,000and6,000thousanddollars?The required probability = 0.2978(c) How much did a golfer have to earn to be in the top 25% of the incomebracket?The requiredcut-off value=$5,893.592 thousands = $5,893,592d. What is the probability that a golfer earned less than 2, 000 thousanddollars?The required probability = 0.18672. (Comparing random samples and populations). Open the Excelfile EAI.xlsx. Thedata showthe annual salary for all 2, 500 managers in one company. Construct arandom sample of 100managers and answer the following questions.(a) Find a point estimate of the mean annual salary from the random sample youhaveconstructed.The point estimate of the mean annual salary from the random sample constructed is thesample mean.๐เท=๐‘ฟเดฅ=$๐Ÿ“๐Ÿ,๐Ÿ“๐Ÿ๐Ÿ•.๐Ÿ๐Ÿ—(b) Find a point estimate of the population standard deviation for annual salaryfrom the randomsample youhave constructed.The point estimate of the population standard deviation for annual salary from the randomsample constructed is the samplestandard deviation.

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