1. (20 points) The television show NBC Sunday Night Football broadcasted a game

Question

1. (20 points) The television show NBC Sunday Night Football broadcasted a game between the Colts and Patriots and received a share of 22, meaning that 22% of the TV sets in use were tuned to that game. An advertiser wants to obtain a second opinion by conducting its own survey using 20 households. a) Find the probability that exactly 2 of the households are tuned to NBC Sunday Night Football. b) Find the probability that at least three households are tuned to NBC Sunday Night Football. c) Find the probability that at most three households are tuned to NBC Sunday Night Football. d) Find the probability that more than 4 households are tuned to NBC Sunday Night Football.

Explanation / Answer

X ~ Binomial (n,p)

Where n = 20 , p = 0.22

Binomial Probability distribution is

P(X) = nCx px (1 - p)n-x

a)

P( X = 2) = 20C2 0.222 0.7818

= 0.1050

b)

P( X >= 3) = 1 - P( X <= 2)

= 1 - [ P( X = 0) + P( X = 1) + P( X = 2) ]

= 1 - [ 20C0 0.220 0.7820 +20C1 0.221 0.7819 +20C2 0.222 0.7818 ]

= 1 - 0.1512

= 0.8488

c)

P( X <= 3) = P( X = 0) + P( X = 1) + P( X = 2) + P(X = 3)

= 20C0 0.220 0.7820 +20C1 0.221 0.7819 +20C2 0.222 0.7818 + 20C3 0.223 0.7817

= 0.3289

d)

P( X > 4) = 1 - P( X <= 4)

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

= 1 - [ 20C0 0.220 0.7820 +20C1 0.221 0.7819 +20C2 0.222 0.7818 + 20C3 0.223 0.7817 + 20C4 0.224 0.7816]

= 1 - 0.5420

= 0.4580

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.