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Chapter 6: Q. 1.1 (page 385)

For each of the following situations, determine whether the given random variable has a binomial distribution. Justify your answer.

1. Shuffle a deck of cards. Turn over the top card. Put the card back in the deck, and shuffle again. Repeat this process 10 times.

Let X=the number of aces you observe.

Short Answer

Expert verified

Yes, the given statement is a binomial distribution.

Step by step solution

01

Given Information

Given in the question that, we have to shuffle a deck of cards. Turn over the top card. Put the card back in the deck, and shuffle again. Repeat this process 10 times.

X=Number of aces you observe.

02

Explanation

A single trial does not influence the outcome of any other trial since the cards are replaced and shuffled each time.

In advance, 10trials are set.

The probability of success is 452for each trial.

It is a binomial setting.

This is a binomial random variable since Xcounts the number of successes, n=10and p=452

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