Question

TV Ratings The television show Cold Case has a 15 share, meaning that while it is being broadcast, 15% of the TV sets in use are tuned to Cold Case (based on data from Nielsen Media Research). A special focus group consists of 12 randomly selected households (each with one TVset in use during the time of a Cold Case broadcast). a. What is the expected number of sets tuned to Cold Case? b. In such groups of 12, what is the mean number of sets tuned to Cold Case? c. In such groups of 12, what is the standard deviation for the number of sets tuned to Cold Case? d. For such a group of 12, find the probability that exactly 3 TVsets are tuned to Cold Case. e. For such a group of 12, would it be unusual to find that no sets are tuned to Cold Case? Why or why not?

Answer 1

here this is binomial with parameter n=12 and p=0.15

a)

expected number of sets tuned to Cold Case =np =12*0.15 =1.80

b)

mean number of sets tuned to Cold Case np =12*0.15 =1.80

c)

standard deviation σ=√(np(1-p))=1.2369

d)

P(X=3)=

(12C3)0.153(1−0.15)(12-3)    =

0.1720

e)

P(X=0)=

(12C0)0.150(1−0.15)(12-0)    =

0.1422

since the probability of this event is not less than 0.05 , this event cannot be termed as unusual