Question

Chapter 5: Discussions 1. Scheduling Employees: Suppose you own a catering company. You hire temporary employees to act as servers from the local college. Not being the most reliable employees, there is an 80% chance that any one server will actually show up for a scheduled event. For a wedding scheduled on a given Saturday you need at least 5 servers. (a) Suppose you schedule 5 employees, what is the probability that all 5 come to work? (b) Suppose you schedule 7 employees, what is the probability that at least 5 come to work? c) How many employees should you schedule in order to be 99% confident that at least 5 come to work? Hint: There is no single formula for the answer to this problem, you should use some type of trial and error 2. Resolving Probabilities of Exactly One and At Least One: Suppose the US Transportation Security Administration (TSA) requires 10% of all airplane passengers be randomly selected for a full screening before boarding a plane. Now, suppose you will travel on a plane 8 times in the coming year. (a) What is the probability that you will get screened exactly once? (b) What is the probability that you will get screened at least once? (c) Is the probability in favor (>50%) of you getting screened exactly once? Is the probability in favor (>50%) of you getting screened at least once? 3. Fair Coin: Suppose you want to test a coin to see if it is fair or not. You do this by flipping it 40 times. You will deem it unfair if the number of heads is unusual. What would be the acceptable range of heads to let the coin pass as fair? Assume, at first, that the coin is fair.

Answer 1

1.)

let x be the employees come to work

Here X follows the binomial probability with p=0.80

a.)

n=5,p=0.8 P(X = 5) = 0.32768

(use excel function:=BINOMDIST(5,5,0.8,0))

b.)n=7, p=0.8

P(X > 5) = P(X = 5) + P(X = 6) + P(X = 7) = 1 - P(X < 4) = 1 – 0.1480 (use excel function := BINOMDIST(4,7,0.8, TRUE)) = 0.8520

c.)

for n=7

p=85.20%

for n=8

P(X > 5) = P(X = 5) + P(X = 6) + P(X = 7) = 1 - P(X < 4) = 1-0.0563 (use excel function := BINOM DIST(4, 8,0.8, TRUE)) = 0.9437

=94.37

n=9

P(x > 5) = P(X = 5) + P(X = 6) + P(X = 7) = 1 - P(X < 4) = 1 – 0.0196 (use excel function := BINOM DIST(4,9,0.8, TRUE)) = 0.9804

=98.04%

Ans:9