It is reported that 23 of American households use a cell pho

It is reported that 23% of American households use a cell phone exclusively for their telephone service. In a sample of fifteen households, find the probability that:

No household uses a cell phone as their exclusive telephone service. (Round your answer to 4 decimal places.)

Exactly 9 households exclusively use a cell phone for telephone service. (Round your answer to 4 decimal places.)

Find the mean number of households exclusively using cell phones. (Round your answer to 4 decimal places.)

Solution

Let X be a random variable .

X i s the no. of households that use a cell phone exclusively for their telephone service.

a) probability that No household uses a cell phone as their exclusive telephone service = P(X=0)

                                                                                                                                          = 15C0 * 0.23⁰ * 0.77¹⁵

                                                                                                                                         = 0.0198

b) probability that Exactly 9 households exclusively use a cell phone for telephone service = P(X=9)

                                                                                                                                                = 15C9 * 0.23⁹ * 0.77⁶

                                                                                                                                                =1.8789 * 10^-3

c) P(X=0) = 15C0 * 0.23⁰ * 0.77¹⁵ = 0.0198

P(X=1) = 15C1 * 0.23¹ * 0.77¹⁴ = 0.0889

P(X=2) = 15C2 * 0.23² * 0.77¹³ = 0.1858

P(X=3) = 15C3 * 0.23³ * 0.77¹² = 0.2405

P(X=4) = 15C4 * 0.23⁴ * 0.77¹¹ = 0.2155

P(X=5) = 15C5 * 0.23⁵ * 0.77¹⁰ = 0.1416

P(X=6) = 15C6 * 0.23⁶ * 0.77⁹ = 0.0705

P(X=7) = 15C7 * 0.23⁷ * 0.77⁸ = 0.0271

P(X=8) = 15C8 * 0.23⁸ * 0.77⁷ = 8.0874 * 10^-3

P(X=9) = 15C9 * 0.23⁹ * 0.77⁶ = 1.8789 * 10^-3

P(X=10) = 15C10 * 0.23¹⁰ * 0.77⁵ = 3.3673 * 10^-4

P(X=11) = 15C11 * 0.23¹¹ * 0.77⁴ = 4.5720 * 10^-5

P(X=12) = 15C12 * 0.23¹² * 0.77³ = 4.5522 * 10^-6

P(X=13) = 15C13 * 0.23¹³ * 0.77² = 3.1379 * 10^-7

P(X=14) = 15C14 * 0.23¹⁴ * 0.77¹ = 1.3390 * 10^-8

P(X=15) = 15C15 * 0.23¹⁵ * 0.77⁰ = 2.6664 * 10^-10

mean = 0 * 0.0198 + 1 * 0.0889 + 2 * 0.1858 + 3 * 0.2405 + 4 * 0.2155 + 5 * 0.1416 + 6 * 0.0705 + 7 * 0.0271 + 8 * 8.0874 * 10^-3 + 9 * 1.8789 * 10^-3 + 10 * 3.3673 * 10^-4 + 11 * 4.5720 * 10^-5 + 12 * 4.5522 * 10^-6 + 13 * 3.1379 * 10^-7 + 14 * 1.3390 * 10^-8 + 15 * 2.6664 * 10^-10

= 3.4435 (ANS)