Question

Forty percent of business travelers carry either a cell phone or a laptop. For a sample of 15 business travelers, make the following calculations.

a. Compute the probability that three of the travelers carry a cell phone or laptop.

b. Compute the probability that 12 of the travelers carry neither a cell nor a laptop.

c. Compute the probability that at least three of the travelers carry a phone or a laptop.

Answer 1

First of all check whether all assumptions of binomial distribution is satisfied or not -

The four characteristic of binomial distribution is -

1)The number of observations n=15 is fixed.
2)Each observation is independent.
3)Each observation represents one of two outcomes ("Carry " or " not carry").
4)The probability of "success" p=0.4 is the same for each outcome.

To get the probability the respective probabilities
consider, X- Number of business travelers carry either a cell phone or a laptop
Then X~Bin(15,0.4)
a) probability that three of the travelers carry a cell phone or laptop= P(X=3) =0.0634
( This is obtained using the excel command "=Binomdist(number,trail,probability,cumulative)",here number=3,trail =15 ,probability =0.4 ,cumulative = False in above command)

b) probability that 12 of the travelers carry neither a cell nor a laptop= 1- P(X=12) =1-0.0016=0.9984
( This is obtained using the excel command "=Binomdist(number,trail,probability,cumulative)",here number=12,trail =15 ,probability =0.4 ,cumulative = False in above command)

c) probability that at least three of the travelers carry a phone or a laptop= P(X<=3) =0.0905

( This is obtained using the excel command "=Binomdist(number,trail,probability,cumulative)",here number=3,trail =15 ,probability =0.4 ,cumulative = True in above command)