Question

Identify the parameter p in the following binomial distribution scenario. The probability of buying a movie ticket with a popcorn coupon is 0.676, and the probability of buying a movie ticket without a popcorn coupon is 0.324. If you buy 25movie tickets, we want to know the probability that more than 16 of the tickets have popcorn coupons. (Consider tickets with popcorn coupons as successes in the binomial distribution.)

Answer 1

Identify the parameter p in the following binomial distribution scenario. The probability of buying a movie ticket with a popcorn coupon is 0.676, and the probability of buying a movie ticket without a popcorn coupon is 0.324. If you buy 25movie tickets, we want to know the probability that more than 16 of the tickets have popcorn coupons. (Consider tickets with popcorn coupons as successes in the binomial distribution.)

Proportion of tickets with popcorn coupons = p= 0.676

n=25

Expectation = np = 16.9

Variance = np(1 - p) = 5.4756

Standard deviation = 2.34

We use normal distribution approximate to binomial to find the required probability.

With continuity correction , z value for more than 16 is z = ( 16.5-16.9)/2.34

= -0.17

P( x >16) = P( z > -0.17)

=0.5675

Excel function used; =1-NORM.S.DIST(-0.17,TRUE)

Note: if we use binomial distribution to find the probability, Then p value is 0.5773