[AP Statistics] 6.3a Binomial Random Variables

Genetics says that the genes children receive from their parents are independent from one child to another. Each child of a particular set of parents has probability 0.25 of having type O blood. Suppose these parents have 5 children. Count the number of children with type O blood.

Determine whether the random variable has a binomial distribution. Justify your answer.

Shuffle a standard deck of 52 playing cards. Turn over the first 10 cards, one at a time. Record the number of aces you observe.

Determine whether the random variable has a binomial distribution. Justify your answer.

Shuffle a deck of cards. Turn over the top card. Put the card back in the deck, and shuffle again. Repeat this process until you get an ace. Count the number of cards you had to turn over.

Determine whether the random variable has a binomial distribution. Justify your answer.

As a special promotion for its 20-ounce bottles of soda, a soft drink company printed a message on the inside of each bottle cap. Some of the caps said, “Please try again!” while others said, “You’re a winner!” The company advertised the promotion with the slogan “1 in 6 wins a prize.” The prize is a free 20-ounce bottle of soda.

Allie’s statistics class wonders if the company’s claim holds true for the bottles at a nearby convenience store. To find out, all 30 students in the class go to the store and each student buys one 20-ounce bottle of the soda. Two of them get caps that say, “You’re a winner!”

What is the probability that exactly two students win?

Round to 3 decimal places.

What is the probability that one or fewer students win?

Round to 3 decimal places.

Does this result give convincing evidence that the company’s 1-in-6 claim is inaccurate? Explain

What is the probability of 10 or more students winning?

Round to 2 decimal places.

As a special promotion for its 20-ounce bottles of soda, a soft drink company printed a message on the inside of each bottle cap. Some of the caps said, “Please try again!” while others said, “You’re a winner!” The company advertised the promotion with the slogan “1 in 6 wins a prize.” The prize is a free 20-ounce bottle of soda.

Allie’s statistics class wonders if the company’s claim holds true for the bottles at a nearby convenience store. To find out, all 30 students in the class go to the store and each student buys one 20-ounce bottle of the soda. Two of them get caps that say, “You’re a winner!”

Calculate and interpret the mean of X

Calculate and interpret the Standard Deviation of X

Determine whether the random variable has a binomial distribution. Justify your answer.

Determine whether the random variable has a binomial distribution. Justify your answer.

Just put the value below.

Round to 2 decimal places.

Interpret your answer to #12

What is the probability that more than 4 elk survive to adulthood?

Round to 2 decimal places.

Round to 2 decimal places.

Calculate P(X≤7)

Round to two decimal places

Round to 2 decimal places.

Round to 2 decimal places.

Calculate the mean of X

Round to 2 decimal places.

Interpret the mean of X

Calculate the standard deviation of X

Round to 2 decimal places.

Interpret the standard deviation of X

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