Question

Consumer Reports rated airlines and found that 80% of the flights involved in the study arrived on time (i.e., within 15 minutes of scheduled arrival time). Assuming that the on-time arrival rate is representative of the entire commercial airline industry, consider a random sample of 214 flights. (Round your answers to two decimal places.)

What is the expected number that will arrive on time?


What is the standard deviation of this distribution?

The Orchard Cafe has found that about 6% of the diners who make reservations don't show up. If 83 reservations have been made, how many diners can be expected to show up? Find the standard deviation of this distribution. (Round your answers to two decimal places.)

μ =
σ =

Answer 1

If X follows Binomial distribution with parameter n and p then

Expected value = = np

Standard deviation = =

a)

Let , X be the number of flight arrive on time.

p =80% = 0.8 , n = 214

X follows Binomial distribution with n=214 and p = 0.8

So,

Expected number that will arrive on time = n*p = 214*0.8 = 171.2

b)

Let , X be the number of diners who make reservations don't show up

p = 6% = 0.06 , n = 83

So,

Expected value =   = np = 83*0.06 = 4.98

Standard deviation :

=