Question

Does the kid factor make a difference? If you are talking photography, the answer may be yes!

Ages of children in household, years	Under 2	None under 21
Percent of U.S. households that buy film	70%	30%

Let us say you are a market research person who interviews a random sample of 8 households.

(a) Suppose you interview 8 households with children under the age of 2 years. Let r represent the number of such households that buy film. Make a histogram showing the probability distribution of r for r = 0 through r = 8.

Find the mean and standard deviation of this probability distribution. (Round your answers to two decimal places.)

μ =  households

σ =  households

(b) Suppose that the 8 households are chosen to have no children under 21 years old. Let r represent the number of such households that buy film. Make a histogram showing the probability distribution of r for r = 0 through r = 8.

Find the mean and standard deviation of this probability distribution. (Round your answers to two decimal places.)

μ =  households

σ =  households

(c) Compare the distributions in parts (a) and (b). You are designing TV ads to sell film. Could you justify featuring ads of parents taking pictures of toddlers? Explain your answer.

A Yes. It appears that households with children under 2 are more likely to buy film.

B No. It appears that households with children under 2 are more likely to buy film.

C No. It appears that households with no children under 21 are more likely to buy film.

D Yes. It appears that households with no children under 21 are more likely to buy film.

Answer 1

a)

Mean = np =    8*0.7=       5.600

Standard deviation = √(np(1-p)) =   √(8*0.7*(1-0.7))=       1.30

  
P ( X = 0) = C (8,0) * 0.7^0 * ( 1 - 0.7)^8=      0.0001
P ( X = 1) = C (8,1) * 0.7^1 * ( 1 - 0.7)^7=      0.0012
P ( X = 2) = C (8,2) * 0.7^2 * ( 1 - 0.7)^6=      0.0100
P ( X = 3) = C (8,3) * 0.7^3 * ( 1 - 0.7)^5=      0.0467
P ( X = 4) = C (8,4) * 0.7^4 * ( 1 - 0.7)^4=      0.1361
P ( X = 5) = C (8,5) * 0.7^5 * ( 1 - 0.7)^3=      0.2541
P ( X = 6) = C (8,6) * 0.7^6 * ( 1 - 0.7)^2=      0.2965
P ( X = 7) = C (8,7) * 0.7^7 * ( 1 - 0.7)^1=      0.1977
P ( X = 8) = C (8,8) * 0.7^8 * ( 1 - 0.7)^0=      0.0576

b)

Mean = np =    8*0.3=       2.400

Standard deviation = √(np(1-p)) =   √(8*0.3*(1-0.3))=       1.2961

P ( X = 0) = C (8,0) * 0.3^0 * ( 1 - 0.3)^8=      0.0576
P ( X = 1) = C (8,1) * 0.3^1 * ( 1 - 0.3)^7=      0.1977
P ( X = 2) = C (8,2) * 0.3^2 * ( 1 - 0.3)^6=      0.2965
P ( X = 3) = C (8,3) * 0.3^3 * ( 1 - 0.3)^5=      0.2541
P ( X = 4) = C (8,4) * 0.3^4 * ( 1 - 0.3)^4=      0.1361
P ( X = 5) = C (8,5) * 0.3^5 * ( 1 - 0.3)^3=      0.0467
P ( X = 6) = C (8,6) * 0.3^6 * ( 1 - 0.3)^2=      0.0100
P ( X = 7) = C (8,7) * 0.3^7 * ( 1 - 0.3)^1=      0.0012
P ( X = 8) = C (8,8) * 0.3^8 * ( 1 - 0.3)^0=      0.0001

c)

A Yes. It appears that households with children under 2 are more likely to buy film.