Statistics and Probability with Applications

Which of the following is not a random variable?

• The heights of randomly-selected buildings in New York City.

• The suit of a card randomly-selected from a 52-card deck.

• The number of children in randomly-selected households in the United States.

• The amount of money won (or lost) by the next person to walk out of a casino in Las Vegas.

A random variable is

• a hypothetical list of the possible outcomes of a random phenomenon.
• any phenomenon in which outcomes are equally likely.
• any number that changes in a predictable way in the long run.
• a variable whose value is a numerical outcome associated with a random phenomenon.

In a particular game, a fair die is tossed.  If the number of spots showing is either 4 or 5 you win $1, if the number of spots showing is 6 you win $4, and if the number of spots showing is 1, 2, or 3 you win nothing.  Let X be the amount that you win. 
Which of the following is the expected value of X?

• $1.00
• $2.50
• $4.00
• $6.00

A small store keeps track of the number X of customers that make a purchase during the first hour that the store is open each day.  Based on the records, X has the following probability distribution.
The mean number of customers that make a purchase during the first hour that the store is open is:
   

• 2.0
• 2.5
• 2.9
• 3

A college basketball player makes 5/6 of his free throws. Assuming free throw attempts are independent, the probability that he makes exactly three of his next four free throws is

• 4(1/6)³(5/6)¹
• (1/6)³(5/6)¹
• (1/6)¹(5/6)³
• 4(1/6)¹(5/6)³

Barry Bonds has a career batting average of .298.  What is the probability that he will get on base 6 times in 10 at bats?

• 3.58%
• 5.46%
• 22.67%
• 100%

The American Red Cross says that about 11% of the U.S. population has Type B blood. A blood drive is being held at your school.What is the probability that exactly 2 of the first 20 blood donors have Type B blood? 

• 0.316
• 0.282
• 0.001
• Not here

What does the p stand for in the binomial probability formula?

• Number of trials
• Number of Successes
• Probability of Successes
• Probability of Failures

The table represents the probability of guessing correct on a 5 question true-false quiz.  Find the probability for at least 4 questions correct.

• .03125
• .15625
• .3125
• .1875

 The standard deviation of X is σ_X=1.08 where X represents the number of cars for a household. If many households were selected at random, which of the following would be the best interpretation of the value 1.08?

• The mean number of cars would be about 1.08
• The number of cars would typically vary by about 1.08 from the mean
• The number of cars would be at most 1.08 from the mean
• the number of cars would be within 1.08 from the mean about 68% of the time