Should you use the binomial distribution? In each of the following situations, i

Question

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

Explanation / Answer

(a)

Here X has binomial disteibution becuase each trials (each person) is independent from each other. And there is only two possible outcomes for each trial (Yes or no). Parameters are n=200 and p=0.5

(b)

Here X is not binomial random variable. Becuase X counts the number of tosses until head appears. So probabaility of success vary from one trial to other.

(c)

Here X has binomial disteibution becuase each trials (each person) is independent from each other. And there is only two possible outcomes for each trial (either reached or not reached). Parameters are n=500 and p=1/12

(d)

Since a deck of cards has 26 black card and 26 red cards so here X has binomial disteibution with probabaility of success p =26/52 = 0.5 and n=10.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---