Question

A TV​ show, Lindsay and Tobias​, recently had a share of 20​, meaning that among the TV sets in​ use, 20​% were tuned to that show. Assume that an advertiser wants to verify that 20​% share value by conducting its own​ survey, and a pilot survey begins with 16 households having TV sets in use at the time of a Lindsay and Tobias broadcast.

a. Find the probability that none of the households are tuned to Lindsay and Tobias.

b. Find the probability that at least one household is tuned to Lindsay and Tobias

c. Find the probability that at most one household is tuned to Lindsay and Tobias

d. If at most one household is tuned to Lindsay and Tobias​,

does it appear that the 25​% share value is​ wrong? Why or why​not?

A.​No, because with a 25​% ​rate, the probability of at most one household is less than 0.05.

B.​Yes, because with a 25​% ​rate, the probability of at most one household is greater than 0.05.

C. Yes​,because with a 25​% ​rate, the probability of at most one household is less than 0.05.

D. No, because with a 25​% ​rate, the probability of at most one household is greater than 0.05.

Answer 1

(hi, in this question, on top 20% share is given and in part d) it is given as 25%, i am doing this with 20%, please reply if it is 25%)

here this is binomial with parameter n=16 and p=0.2

a)

P(X=0)=

(nCx)px(1−p)(n-x)    = 0.8^16=

0.0281

b)

P(X>=1)=1-P(X<=0)=

0.9719

C)

P(X<=1)=

∑x=0a     (nCx)px(1−p)(n-x)    =

0.1407

d)

D. No, because with a 25​% ​rate, the probability of at most one household is greater than 0.05.