Chapter 05, Section 5.4, Problem 029 Select each of the following experiments th

Question

Chapter 05, Section 5.4, Problem 029 Select each of the following experiments that are binomial experiments Drawing 3 balls without replacement from a box Selecting a few households from New York City and observing whether or not they own stocks when it is known that 4 % of all households in New York City own stocks. Drawing 3 balls with replacement from a box that contains 13 balls, 4 of which are red and 9 are blue, and observing the colors of the drawn balls that contains 13 balls, 4 of which are red and 9 are blue, and observing the colors of the drawn balls Click if you would like to Show Work for this question:

Explanation / Answer

first is the only choice of binomial experiment.

As we know that the binomial distribution has the following formula

P(X=x) = nCx * p^x * q^(n-x)

here we have n=13 total balls , x=3 drawing balls without replacement

4 are of red color and 9 are of blue color

Now we may want to observe the event of blue

then the probability of success is p=9/13 and prob of failure is q=4/13 and we can put all the events in the above equation and solve

while for second option we don't have any of these values available as it's a test of Poission distribution

and in the case of last one where we have replacements allowed it's a Hyper Geometric distribution and hence we can't apply binomial theorm.

So.,

first is the only choice of binomial experiment.

Hope the above answer has helped you in understanding the problem. Please upvote the ans if it has really helped you. Good Luck!!

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