hich of the following are binomial random variables? Justify why or why not. (a)
ID: 3371376 • Letter: H
Question
hich of the following are binomial random variables? Justify why or why not. (a) The number of traffic accidents in a given town during a 30 day period. (b) The number of successful heart transplants out of 35 completed at a particular hospital. (c) The number of construction projects that failed inspection out of the 723 inspected during 1997 8.9. CHAPTER 8 EXERCISES 203 (d) The number of shoplifting charges filed in municipal court in your city during 1997. (e) Fifteen cookies are dropped into a bag, eight oatmeal and seven chocolate chip. Let C be the number of chocolate chip cookies observed in five draws. You will choose a cookie from the bag, observe the kind of cookie it is, then eat it and draw again. (o) A safety road block wil b in place on a road for four hours. Every third car will e stopped. Let R be the number of cars stopped that are red (8) A sample of 25 women will be taken. Let Y be the number of women sampled who have never been married amount of time it takes before 10 babies are born. Let the random variable G be the number of girl babies you observe. (h) In an effort to study the gender of babies in a local hospital, you will go to the hospital and measure theExplanation / Answer
5. (a) Number of traffic accidents in a given town during a 30
day period will follow Binomial distribution as there are two
possibilities: either accident will happen or it will not. Here, the
distribution is Bin(30, p), where, p is the probability of an
accident. (Ans).
(b) Here, either heart transplant will be successful or it will not.
So there are two possible outcomes and the distribution is
Bin(35, p). p is the probability of success. (Ans).
(c) Here, either inspection will happen or not. Since there are
two possible outcomes, the distribution is Binomial (723, p),
p is the probability of success. (Ans).
(d) The distribution is not Binomial in this case. (Ans).
(e) Here, the distribution is not Binomial, as the total number
of cookies change after each draw. So the trials are not
independent. (Ans).
(f) Here the trials are not independent, so the distribution is
not Binomial. (Ans).
(g) Here, Y ~ Bin(25, p), p is the probability of neven been
married. So the distribution is Binomial. (Ans).
(h) Here the distribution is not Binomial. (Ans).
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