AP Statistics Binomial and Geometric Probability

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 10 times. Let X = the number of aces you observe.

• Yes
• No, the trials are not independent.
• No, there are more than 2 outcomes

Which of the following is NOT an assumption of the Binomial distribution?

• All trials must be independent.
• Each trial must be classified as a success or a failure.
• All trials are dependent on each other.
• The number of successes in the trials is counted.

A geometric probability model follows a Bernoulli trial and:

• Has a set sample size n.
• Is looking for first success

It has been estimated that about 30% of frozen chicken contain enough salmonella bacteria to cause illness if improperly cooked. If 12 frozen chickens are bought, how many are expected to contain enough salmonella bacteria to cause illness if improperly cooked? What is the standard deviation?

• Mean = 3.33 St. Dev. = 1.59

• Mean = 3.33 St. Dev. = 2.79

• Mean = 3.6 St. Dev. = 1.59

• Mean = 3.6 St. Dev. = 2.79

It has been estimated that about 30% of frozen chicken contain enough salmonella bacteria to cause illness if improperly cooked. How many would a consumer expect to buy until she gets her first contaminated chicken?

• 3

• 3.33

• 3.6

• 2.52

It has been estimated that about 30% of frozen chicken contain enough salmonella bacteria to cause illness if improperly cooked. What is the probability a consumer will find his first contaminated chicken on the 5th chicken he buys?

• 0.00567

• 0.8821

• 0.072

• 0.168

It has been estimated that about 30% of frozen chicken contain enough salmonella bacteria to cause illness if improperly cooked. A consumer purchases 12 frozen chickens. What is the probability that the consumer will have more than 6 contaminated chickens? 

• .961
• .118
• .882
• .039

It has been estimated that about 30% of frozen chicken contain enough salmonella bacteria to cause illness if improperly cooked. A consumer purchases 12 frozen chickens. What is the probability that the consumer will have exactly 6 contaminated chickens?

• .079

• .118

• .882

• .039

It has been estimated that about 30% of frozen chicken contain enough salmonella bacteria to cause illness if improperly cooked. A consumer purchases 12 frozen chickens. What is the probability that the consumer will have at least 2 contaminated chickens?

• .079

• .118

• .915

• .039

It has been estimated that about 30% of frozen chicken contain enough salmonella bacteria to cause illness if improperly cooked. A consumer purchases 12 frozen chickens. What is the probability that at most 4 are contaminated chickens?

• .079

• .118

• .724

• .675