Random Variables and Distributions

A discrete random variable X has the probability distributions shown in the table. Find the value of k. (Remember that a valid probability distribution must add up to 1)

• 1/3

• 7/12

• 1/12

• 1/4

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

A marketing survey compiled data on the number of cars in households.  If X = the number of cars in a randomly selected household, and we omit the rare cases of more than 5 cars, then X has the following probability distribution: 
X           0          1          2          3           4           5    
P(X)   0.24    0.37    0.20    0.11    0.05     0.03
What is the probability that a randomly chosen household has at least two cars?

• 0.20

• 0.29

• 0.39

• 0.61

An algebra 2 test has 6 multiple choice questions with four choices with one correct answer each. If we just randomly guess on each of the 6 questions, what is the probability that you get exactly 3 questions correct? (You need to figure out the p value first. It is not given to you.)

• 96.2%

• 13.2%

• 8.31%

• 25.0

If you were to flip a coin 20 times, what is the probability you would get exactly 10 heads?

• 50%

• 17.62%

• .58.81%

• 41.19%

When rolling two dice, the probability of rolling doubles is ⅙. Suppose that a game player rolls the dice five times, hoping to roll doubles. Find the probability that the player gets doubles exactly twice in 5 attempts.

• 0.884

• 0.139

• 0.965

• 0.161

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 at least 2 of the first 10 blood donors has Type B blood? 

• 0.088

• 0.697

• 0.214

• 0.303 

Find the mean of a binomial distribution with n=50 and p=0.4

• 50

• 4

• 20

• 10

Is this binomial experiment? Shuffle a deck of 52 cards. Turn over the top card. Put the card back in the deck, shuffle again. Repeat the process 50 times. Let X = the number of aces you observe.

• Yes

• No, the trials are not independent.

• No, there are more than 2 outcomes

The table above shows the number of cell phones per household in a small town. Find the mean round to the nearest hundredth.

• 2.80

• 2.93

• 0.10

• 0.14