5.21 Should you use the binomial distribution? In each of the following situatio

Question

5.21 Should you use the binomial distribution? In each of the following situations, is it reasonable to use a binomial distribution for the random variableX Give reasons for your answer in each case. If a bino- mial distribution applies, give the values of n and p. (a) A poll of 200 college students asks whether or not they usually feel irritable in the morning. X is the numbe who reply that they do usually feel irritable in the morning (b) You toss a fair coin until a head appears. X is the count of the number of tosses that you make. (e) Most calls made at random by sample surveys tot succeed in talking with a person. Of calls to New York only one-twelfth succeed. A survey calls 500 ranr selected numbers in New York City. X is the n times that a person is reached. (d) You deal 10 cards from a shuffled deck of saards playing cards and count the number X of blac City randomly

Explanation / Answer

Solution-

1. Binomial distribution can be used here as 200 students are fixed and independent. Plus, it measures the number of success as- feeling irritable in the morning.

2. Binomial can not be used here as it does not measure the number of successes. Infact it measures the number of times needed to get first success.

3. Binomial distribution can be used here as 200 numbers are fixed and independent. Plus, it measures the number of success as- reaching to a person and probability of this outcome is also fixed.

4. Binomial distribution can be used here as events black or red are independent. Plus, it measures the number of success as- getting black with a fixed probability of 1/2 in each success.

Answers

TY!

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