Question

You are working at a movie theatre selling popcorn and notice that 70% of the moviegoers prefer buttered popcorn. You decide to conduct an experiment on the next 10 moviegoers. (Hint…this is a binomial problem) A) what is the probability that only 2 of the next 10 moviegoers will order buttered popcorn? B) What is the probability that 5 of the next 10 moviegoers will order buttered popcorn? C) What is the expected value, variance and standard deviation of your experiment?

Answer 1

Answer)

As there are fixed number of trials and probability of each and every trial is same and independent of each other

Here we need to use the binomial formula

P(r) = ncr*(p^r)*(1-p)^n-r

Ncr = n!/(r!*(n-r)!)

N! = N*n-1*n-2*n-3*n-4*n-5........till 1

For example 5! = 5*4*3*2*1

Special case is 0! = 1

P = probability of single trial = 70%

N = number of trials = 10

R = desired success

A)

P(2) = 10c2*(0.7^2)*(1-0.7)^10-2 = 0.0014467005

B)

P(5) = 0.1029193452

C)

Expected value = n*p = 10*0.7 = 7

Variance = n*p*(1-p) = 2.1

S.d = √variance = √2.1 = 1.44913767461