Question

suppose you own a retail business and you read that 20% of retail employees, when reporting the he amount of time they worked on any given day, actually lie about the time they worked. you have 9 employees and you are going to monitor the time sheets of your employees to see if they actually lie on their sheets. if you find that three or more of your employees do lie, you will you will be very angry! Based on this information suppose you have 40 employees. calculate the probability of three or more of your employees lie on their time sheets.

Answer 1

n = 40

p = 0.2

It is a binomial distribution.

P(X = x) = nCx * p^x * (1 - p)^{n - x}

P(X > 3) = 1 - P(X < 3)

              = 1 - (P(X = 0) + P(X = 1) + P(X = 2))

              = 1 - (40C0 * (0.2)^0 * (0.8)^40 + 40C1 * (0.2)^1 * (0.8)^39 + 40C2 * (0.2)^2 * (0.8)^38)

              = 1 - 0.0079 = 0.9921