Math Help - Probability

A marketing research firm believes that approx. 25% of all persons mailed a sweepstakes offer will respond if a preliminary mailing of 5000 is conducted in a fixed region.

a) What is the probability that 1000 or fewer will respond?

a) What is the probability that 3000 or more will respond?

Originally Posted by r7iris

A marketing research firm believes that approx. 25% of all persons mailed a sweepstakes offer will respond if a preliminary mailing of 5000 is conducted in a fixed region.

a) What is the probability that 1000 or fewer will respond?

a) What is the probability that 3000 or more will respond?

The number of responders has a binomial distribution B(0.25,5000). You are
expected to use the normal approximation.

The mean of the binomial is m=0.25 * 5000 = 1250, and standard deviation
s=sqrt(5000*0.25*0.75) ~= 30.6.

1000 or fewer corresponts to less than a z-score of (1000.5 - m)/s, which
you look up in your normal table (the extra 0.5 is a continuity correction)

3000 of more corresponds to more than a z-score of (2999.5-m)/s.

RonL

For the less than or equal to 1000 question, should it be (999.5-m)/s or (1000.5-m)/s?

Originally Posted by r7iris

For the less than or equal to 1000 question, should it be (999.5-m)/s or (1000.5-m)/s?

No because every thing between 999.5 and 1000.5 rounds to 1000 which is in
the range wanted.

RonL