Question

An airline company operates commuter flights using an aircraft that can take 20 passengers. During each flight passengers are given a hot drink and a Snack Pack that contains a meat sandwich and a cake. The company is aware that some of their passengers may be vegetarians and therefore every flight should be stocked with vegetarian Snack Pack that contains a cheese sandwich in addition to those contain meat. Given that 5% of the population is vegetarian, on a fully booked flight, answer the following questions.                                                                                                                    

a) What is the expected number and standard deviation of vegetarian passenger?

b) What is the probability that there will be exactly one vegetarian passenger? * ANSWER USING EXCEL FUNCTIONS *

c) What is the probability that there will be more than one vegetarian passenger? * ANSWER USING EXCEL FUNCTIONS *

d) What is the probability that there will be no more than two vegetarian passenger? * ANSWER USING EXCEL FUNCTIONS *

Answer 1

An airline company operates commuter flights using an aircraft that can take 20 passengers.

n = 20

5% of the population is vegetarian, on a fully booked flight.

P= 0.05

1)

X: number of vegetarian passenger on a fully booked flight.

X follow binomial with n = 20 & P= 0.05

Mean = n*p = 20*0.05 = 1

std dev = square root ( n*p*(1-p))

=sqaure root( 20*0.05*0.95)

=sqaure root ( 0.95)

= 0.9747

Answer:   expected number = 1 and a standard deviation of vegetarian passenger = 0.9747

The function in excel for binomial probabilities is

" BINOM.DIST(Number, Trials, Probability , Cumulative)"

where number is x value; trials = n, probability = P &

cumulative = 0 if want exact or equal probability

cumulative = 1 if P(X<=x) less than type probability.

b)What is the probability that there will be exactly one vegetarian passenger

P(X = 1 ) = "=BINOM.DIST(1,20, 0.05 , 0) " = 0.377354

(equal prbability so cummulative is 0)

Answer:- 0.377354

c) What is the probability that there will be more than one vegetarian passenger?

P( X > 1) =1- P(x<=1) = "=1- BINOM.DIST(1,20, 0.05 , 1) " =0.26416

(less than type  prbability so cummulative is 1)

Answer:- 0.26416

d) What is the probability that there will be no more than two vegetarian passengers?

P(x>=2) = "=BINOM.DIST(2,20, 0.05 , 1)" = 0.924516

Answer:- 0.924516