Question

A certain TV show recently had a share of ​, meaning that among the TV sets in​ use, ​80% were tuned to that show. Assume that an advertiser wants to verify that ​80% share value by conducting its own​ survey, and a pilot survey begins with 11 households having TV sets in use at the time of the TV show broadcast. Complete parts​ (a) through​ (d) below. Find the probability that all of the households are tuned to the TV show Find the probability that exactly 10 households are tuned to the TV show. Find the probability that at least 10 households are tuned to the TV show. If at least 10 households are tuned to the TV​ show, does it appear that the 80​% share value is​ wrong? Why or why​ not?

Answer 1

Here number of households =n = 11

Probability that people are tuned to that show = p = 0.80

so if x out of 11, then x would follow binomial distribution

x ~ BINOMIAL(n = 11, p = 0.80)

(a) P(All 11 are tuned to that show) = ¹¹C₁₁  (0.80)¹¹ = 0.0860

(b) P(Exactly 10 household will show) = ¹¹C₁₀  (0.80)¹⁰ * 0.2 = 0.2362

(c) P(Atleat 10 houreshold will see the show) = P(x = 10) + P(X = 11) = 0.2362+ 0.0860 = 0.3221

(d) Here as in part(c) we find the probability of that happening greater than 0.05, so we can say that If at least 10 households are tuned to the TV​ show, does it appear that the 80​% share value is​ not wrong, because, it is not an unusual thing to happen.