**
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:

Number of Persons |
Rent-Controlled |
Rent-Subsidized |

1 |
.61 |
.41 |

2 |
.27 |
.30 |

3 |
.07 |
.14 |

4 |
.04 |
.11 |

5 |
.01 |
.03 |

6 |
.00 |
.01 |

Total/Sum |
1.00 |
1.00 |

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

a. what is the probability that the battery life of your iPad

b. what is the probability that the battery life of your iPad

Part 2: Normal Distribution

Part 1: Sampling, Text #3, p. 305

1

**
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.**