Probability & Binomial Distributions CW

Classify: The numbers of cheeseburgers a fast-food restaurant serves each day

• Discrete

• Continuous

Classify: Height of a plant measured each day for 30 days.

• Discrete

• Continuous

Classify: The time it takes for a light bulb to burn out.

• Discrete

• Continuous

Is this a probability distribution?

• No
• Yes

• Yes, because all of the probabilities are between 0 and 1 inclusive and the sum of all the probabilities is 1.
• No, all probabilities are not be between 0 and 1 inclusive
• No, the sum of all the probabilities is not 1.
• Yes, because the distribution is symmetric

1.    Compute the probability of X successes, using the binomial formula.                    

n=10, x = 5, p = 0.37

Answer explanation

0.17

1.    College Education and Business World Success R. H. Bruskin Associates Market Research found that 40% of Americans do not think that having a college education is important to succeed in the business world. If a random sample of 5 Americans is selected, find these probabilities.

a. Exactly 2 people will agree with that statement.

b. At most 3 people will agree with that statement.

Answer explanation

a. 0.34560000

b. 0.2592

0.3456

0.2304

• Yes, because all of the probabilities are between 0 and 1 inclusive and the sum of all the probabilities is 1.
• No, all probabilities are not be between 0 and 1 inclusive
• No, the sum of all the probabilities is not 1.
• Yes, because the distribution is symmetric

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

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