A company surveyed 2,600 North American airline passengers and reported that approximately 75% said that they carry a smartphone when they travel. Suppose that the actual percentage is 75%. Consider randomly selecting six passengers and define the random variable x to be the number of the six selected passengers who travel with a smartphone. The probability distribution of x is the binomial distribution with

n = 6

and

p = 0.75.

(Use SALT. Round your answers to four decimal places.)

(a)

Calculate p(4).

Interpret this probability. Pick One

A. the probability that a random sample of 6 passengers will contain at most 4 passengers who travel with a smartphone

B. the probability that a random sample of 6 passengers will contain at least 4 passengers who travel with a smartphone

C. the probability that a random sample of 6 passengers will contain exactly 4 passengers who travel with a smartphone

D. THE probability that a random sample of 6 passengers will contain more than 4 passengers who travel with a smartphone

E. the probability that a random sample of 6 passengers will contain less than 4 passengers who travel with a smartphone

(b)

Calculate

p(6),

the probability that all six selected passengers travel with a smartphone.

(c)

Calculate

P(x 4).