Economics 2122A Econometrics I Assignment 3

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Question 1 (Show your steps, not only the final results.)

A company produces bags of cypress mulch. The weight in pounds per bag varies as indicated in the following table.

Weight in Pounds	44	45	46	47	48	49	50
P( X)	0.04	0.13	0.21	0.29	0.2	0.1	0.03

a. Calculate the CDF 𝐹(𝑥).

x	𝑥<44	44≤𝑥<45	45≤𝑥<46	46≤𝑥<47	47≤𝑥<48	48≤𝑥<49	49≤𝑥<50	50≤𝑥
𝐹(𝑥)

• What is the probability that a randomly chosen bag will contain more than 45 (> 45) and less than 49 (< 49) pounds of mulch?

• Compute the expectation of the weight.

• The cost of producing a bag of mulch is 20 + 4   cents, where is the number of pounds per bag. The revenue from selling a bag, regardless of weight, is 2.50 dollars. If = − , find the expected profit per bag in dollars using your results from c.

Question 2 (Show your steps, not only the final results.)

According to the PMF table in Question 1, a bag is considered underqualified if it weights less than 47 (< 47). Randomly select three packages. What is the probability that at least one is underqualified (2 points)?

Question 3 (Show your steps, not only the final results.)

Customers arrive at a busy checkout counter at an average rate of 3 per minute. If the distribution of arrivals is Poisson, find the probability that in any given minute there will be 2 or fewer arrivals.

Question 4 (Use the Standard Normal Distribution CDF table) Let the random variable follow a normal distribution with = 80 and ² = 100.

1. Find the probability that is greater than 60.

• Find the probability that is greater than 60 and less than 82.

• The probability is 0.1 that is greater than. What is the value of?

Question 5 (Show your steps, not only the final results.) Consider a population of the years of experience for five employees: 2, 4, 6, 7, 8.

1. Find the population mean.

• If two employees are to be chosen randomly as a sample ( = 2), write down all the possible samples and compute their sample means.

Question 6

List the important formulas you would like to include in your formula sheet.

Related: (Solution) Economics 2122A Econometrics I Assignment 4

Solution – Economics 2122A Econometrics I Assignment 3

What is the probability that a randomly chosen bag will contain more than 45 (>45) and less than 49 (<49) pounds of mulch (2 points)?
Correct Answer: 𝑃(45<𝑋<49) = 𝑃(𝑋=46)+𝑃(𝑋=47)+𝑃(𝑋=48) = 0.7.

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