Normal approx to the binomial dist. questions
An airline finds that 5% of the persons who make reservations on a certain flight do not show up for the flight. If the airline sells 160 tickets for a flight with only 155 seats, what is the probability that a seat will be available for every person holding a reservation and planning to fly?
A1: Let p=0.05, n=160, and .
, which cannot be correct. The correct answer is 0.898, which I am nowhere close to. Where am I going wrong?
Q2: (b) A rancom sample of items is to be selected from a large lot, and the number of defectives is to be observed. What value of guarantees that will be within .1 of the true fraction of defectives, with probability 0.95?
Note: Part (a) of this question showed that the variance of , where has a binomial distribution with n trials and success probability of p, has a maximum at p=0.5, which I was able to show.
A2: Symbolically, I think I need to solve:
, so I want to use the normal approximation to some how come up with a z-value, which I can use to solve for n. Although, when I go down this path I end up with a false equation for n.
Thanks for you help