Does the kid factor make a difference? If you are talking photography, the answe

Question

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

Let us say you are a market research person who interviews a random sample of 10 households.

(a) Suppose you interview 10 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 = 10.

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

(b) Suppose that the 10 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 = 10.

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

(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.

Yes. It appears that households with no children under 21 are more likely to buy film.No. It appears that households with children under 2 are more likely to buy film.    Yes. It appears that households with children under 2 are more likely to buy film.No. It appears that households with no children under 21 are more likely to buy film.

Ages of children in household, years Under 2 None under 21 Percent of U.S. households that buy film 85% 35% 0.25 0.2 0.15 P(r) 0.1 0.05 0 1 2 345 67 8 9 10

Explanation / Answer

a)
X = number of households with children under age of 2 years
X follow binomial disribution with n = 10 , p = 0.85

mean = np = 10*0.85 = 8.5
sd = sqrt(npq) = sqrt(10*0.85*0.15) = 1.12915897906

Binomial with n = 10 and p = 0.85

x P( X = x )
0    0.000000
1    0.000000
2    0.000008
3    0.000126
4    0.001249
5    0.008491
6    0.040096
7    0.129834
8    0.275897
9    0.347425
10    0.196874

correct histogram is D)

b)
similarly here n = 10 , p = 0.35
E(Y) = 10*0.35 = 3.5
sd(Y) = sqrt(10 * 0.35 *0.65) = 1.5083103129

Binomial with n = 10 and p = 0.35

x P( X = x )
0    0.013463
1    0.072492
2    0.175653
3    0.252220
4    0.237668
5    0.153570
6    0.068910
7    0.021203
8    0.004281
9    0.000512
10    0.000028

correct histogram is A)

c)
yes, It appears that households with children under 2 are more likely to buy film.

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