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**Lab 4 | Complete Solution**

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Lab 4

This assignment is due before the end of your Monday/Tuesday section. For every section you will submit your handwritten work to your TA. Only neat and organized assignments will be graded for credit. Take pride in all of your work. Note: you may print plots for your assignment or you can just demonstrate to your TA during section that you can create plots.

1. Open the Excel le GolfIncome.xlsx. The data represent income (in thou- sands of

dollars) earned by a population of 40 professional golfers from their endorsement

deals. Assume that the data follow a normal distribution. Using the NORM.DIST

and NORM.INV functions, determine the following:

(a) What is the probability that a golfer earned more than 3, 000 thousand dollars?

(b) Whatistheprobabilitythatagolferearnedbetween4,000and6,000thousanddollars?

(c) How much did a golfer have to earn to be in the top 25% of the income bracket?

d. What is the probability that a golfer earned less than 2, 000 thousand

dollars?

2. (Comparing random samples and populations). Open the Excel le EAI.xlsx. The

data show the annual salary for all 2, 500 managers in one company. Construct a

random sample of 100 managers and answer the following questions.

(a) Find a point estimate of the mean annual salary from the random sample you

have constructed.

(b) Find a point estimate of the population standard deviation for annual salary

from the random sample you have constructed.

(c) What is the actual population mean annual salary?

(d) What is the actual population standard deviation for annual salary?

(e) What can you observe after nishing parts (a) to (d)?

3. Let X is N ( = 10; = 3). Using a Z table, compute the following:

(a) P(X < 12)

(b) P(X > 9:5)

(c) P(6 < X < 12)

(d) P(X 10 [ X 12)

4. Solve Problem 3 using the NORM.DIST function in Excel. This will output the

cumulative distribution value for N(; ) at point x. In other words, the area under

the normal curve to the left of x.

5. (Using a normal distribution to approximate a binomial distribution). Let X be

Bin(n = 100; = 0:25).

(a) Construct the probability mass function table for random variable X.

(b) Using the probability mass function/table above, calculate P(X 29).

(c) Check to see if we can approximate the distribution of this random variable

with a normal distribution.

(d) Calculate the parameters of the normal distribution that will be used to ap-

proximate the binomial distribution in question.

(e) Using the NORM.DIST function, calculate P(X 28); P(X 28:5); P(X

29); and P(X 29:5).

(f) Which probability best approximates your answer to part (b)? Explain why.

**Lab 4 | Complete Solution**

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