You are told that 90ft of homes donate lo your charitable cause. You have 46 tax

Question

You are told that 90ft of homes donate lo your charitable cause. You have 46 tax receipts left and plan on canvasing a neighborhood having 50 homes (assume that each home making a donation will want a tax receipt). What is the expected number of homes in this neighborhood who will make a donation? What is the probability that you will not run out of receipts before finishing canvasing the neighborhood? What is the probability that you will have receipts left over when you finish canvasing the neighborhood? A friend informs you that at least one home in the neighborhood will not make a donation. If your friend's information is correct, what now is the probability that you will have enough receipts to canvas the neighborhood?

Explanation / Answer

a. expected number is simply 90% (.9) times the number of homes (50).
.9*50=45 homes

b. Use the binomial distribution with n=50 p=.9

Then the probability of not running out of receipts is the probability of having 46 or fewer "successes", given by binomcdf(50,.9,46)=74.97%

c. The probability of running out of receipts is simply 1-the probability of not running out.

1-.7497=25.03%

d. If your friend's information is correct, you only need to consider the 49 houses that could conceivably make donations. The binomial probability then becomes binomcdf(46,.9,49)88%

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