Question

It is reported that 25% of American households use a cell phone exclusively for their telephone service. In a sample of eleven households, find the probability that:

(a)	None use a cell phone as their exclusive service. (Round your answer to 4 decimal places.)

Probability

(b)	At least one uses the cell exclusively. (Round your answer to 4 decimal places.)

Probability

(c)	At least five use the cell phone. (Round your answer to 4 decimal places.)

Probability

Answer 1

n = 11

p = 0.25

It is a binomial distribution.

P(X = x) = nCx * p^x * (1 - p)^{n - x}

a) P(X = 0) = 11C0 * (0.25)^0 * (0.75)^11 = 0.0422

b) P(X > 1) = 1 - P(X < 1)

                  = 1 - P(X = 0)

                  = 1 - (11C0 * (0.25)^0 * (0.75)^11)

                  = 1 - 0.0422 = 0.9578

c) P(X > 5) = 1 - P(X < 5)

                   = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4))

                   = 1 - (11C0 * (0.25)^0 * (0.75)^11 + 11C1 * (0.25)^1 * (0.75)^10 + 11C2 * (0.25)^2 * (0.75)^9 + 11C3 * (0.25)^3 * (0.75)^8 + 11C4 * (0.25)^4 * (0.75)^7)

                  = 1 - 0.8854

                  = 0.1146