Section 6.1 Homework

1. Determine whether the random variable described is discrete or continuous.  The height of a randomly chosen basketball player.

The random variable described is ________

2.  Determine whether the random variable described is discrete or continuous.
The number of heads in 100 tosses of a coin.

The random variable described is ________

3. Determine whether the table represents a discrete probability distribution. Explain why or why not.

The table  ________  represent a discrete probability distribution

4.  Fill in the missing value so that the following table represents a probability distribution.

5.  Fifteen items or less: The number of customers in line at a supermarket express checkout counter is a random variable with the following probability distribution.

(a) Find P(1) =

(b) Find P (No more than 1)

(c) Find the probability that no one is in line.

(d) Find the probability that at least three people are in line.

6.   Put some air in your tires: Let X represent the number of tires with low air pressure on a randomly chosen car. The probability distribution of X is as follows.

(a) Compute the mean

.  . Round the answer to three decimal places as needed.

(b) Compute the standard deviation

.  Round the answer to three decimal places as needed.

7.   Craps: In the game of craps, a pair of dice are rolled, and people bet on the outcome. For example, you can bet $1 that the sum of the dice will be 3 (also called “Ace Deuce”). The probability that you win is

, and if you win, your profit is $15.  If you lose, you lose $1.

(a) What is the expected value of your profit? Round the answer to two decimal places.

The expected value of profit is ______

(b) Is it an expected gain or an expected loss? Round the answer to two decimal places.

This is an expected  ____ of ______

8.   Business projection: An investor is considering an investment in a start-up company. She estimates that she has probability 0.38 of a $15,800 loss, probability 0.26 of a $12,200 profit, probablility 0.12 of a $41,000 profit, and probability 0.24 of breaking even (a profit of $0) What is the expected value of the profit? Would you advise the investor to make the investment?

The expected value of the profit is _____

The investor _____  make the investment 

9.    Insurance: An insurance company sells a 1-year term life insurance policy to a 79 year old woman.  The woman pays a premium of $3000.  If she dies within 1 year, the company will pay $36,000 to her beneficiary. According to the U.S. Centers for Disease Control and Prevention, the probability that an 79-year-old woman will be alive
1 year later is 0.9179.  Let X be the profit made by the insurance company.

(a) Find the probability distribution.   The probability distribution is 

(b) Find the expected value of the profit.  Expected value of the profit is

10.   A cash prize of  $2700 is to be awarded at a fundraiser. If 2700 tickets are sold at $4 each, find the expected value. Round your answer to the nearest cent. 

The expected value is  _____