Econ 3788             Practice Problems 2                Dr. Usip

Please Do The Problems First Before Studying My Solutions.                

Ch. 5: Discrete Probability Distributions (Expected Value & Binomial Problems)
Question 1: ASW, # 23, p. 229
The New York City Housing and Vacancy Survey showed a total of 59,324 rent-controlled housing units and 236,262 rent-stabilized units built in 1947 or later. For these rental units, the probability distribution for the number of persons living in the unit are as follows:

a. What is the expected value of the number persons living in each type of apartment?
b. What is the variance of the number of persons living in each type of apartment?
c. Make some comparison between the number of persons living in rent-controlled units and the number of persons living in rent-subsidized units.

Question 2. A store manager claims that thirty percent of customers who enter the store will make a purchase. Suppose six customers enter the and that these customers make independent purchase decisions.
a. What is the random variable of interest?
b. What is the probability that exactly five customers make a purchase?
c. What is the probability that at least three customers make a purchase?
d. What is the probability that two or fewer customers make a purchase?
e. What is the probability that between three and five customers make a purchase?
f. How many customers would be expected to buy if 3000 customers visit the store in a given day ?

Ch. 6: Continuous Probability Distribution Problems (Uniform & Normal)
Part 1: Uniform Distribution
Some Apple customers prefer iPad Mini to iPad because it is lighter. Assume the battery life of the iPad Mini is uniformly distributed between 8.5 to 12 hours.
1. What is the random variable of interest X?
2. Write the mathematical expression/form of the probability density function (pdf) of X, denoted as f(X).
3. Suppose you recently bought an iPad Mini,
    a. what is the probability that the battery life of your iPad Mini will be 10 hour or less?
    b. what is the probability that the battery life of your iPad Mini will be between 9.5 and 11.5 hours?
    c. For how long would you expect the battery in your iPad Mini to last in a normal day of use?

Part 2: Normal Distribution                  
Automobile repair costs continue to rise with the average cost now at $367 per repair (U.S. News & World Report Website). Assume that the cost for an automobile repair is normally distributed with a standard deviation of $88. Use this information to answer the following questions:
1. What is the probability that the repair cost of an automobile will be more than $450? 
2. What is the probability that the repair cost of an automobile will be less than $250? 
3. What is the probability that the repair cost of an automobile will be between $250 and $450?
4. If the cost for your car repair is in the lower 5% of automobile repair charges, what is your cost? 

Chapter 7: Sampling & Sampling Distribution Problems
Part 1: Sampling, Text #3, p. 305

Part 2: Sampling Distribution of the Sample Mean
1. Would you use the finite population correction factor (FPCF) in calculating the standard error of the mean? Explain.
2. If the population standard deviation is σ = 8.2 years, compute the standard error (i) with the FPCF and (ii) without the FPCF.
3. What is the probability that the sample mean age of the employees will be within ±2 years of the population mean age, μ?

Part 3: Sampling Distribution of the Sample Proportion
Forty-two percent of primary care doctors think that their patients receive unnecessary medical care (Reader's digest, December 2011/January 2012). Suppose a random sample of 300 primary care doctors were taken for this study. Use this information to answer these questions.

1. In words, what is the variable of interest, X, in the context of this problem?
2. Show the sampling distribution of the proportion of doctors who think their patients receive unnecessary medical care.
3. What is the probability that the sample proportion will be within ±.03 of the population proportion?

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Last revised: Tuesday, May 18, 2021.