What is the age distribution of promotion-sensitive shoppers? A supermarket super shopper is defined as a shopper for whom at least 70% of the items purchased were on sale or purchased with a coupon.Age range, years 18-28 29-39 40-50 51-61 62 and overMidpoint x 23 34 45 56 67Percent of super shoppers 6% 47% 21% 12% 14%For the 62-and-over group, use the midpoint 67 years.(a) Using the age midpoints x and the percentage of super shoppers, do we have a valid probability distribution? Explain.(b) Use a histogram to graph the probability(c) Compute the expected age μ of a super shopper. (Round your answer to two decimal places.)μ =

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warylucknow warylucknow · Answer 1 · 2020-03-05T11:10:10+01:00

Answer:

(a) The probability distribution is valid.

(b) The histogram is attached below.

(c) The mean is 33.47.

Step-by-step explanation:

(a)

A probability distribution is valid if:

From the probability distribution table it can be seen that the probability for all x is greater than 0.

Compute the sum of all probabilities as follow:

[tex]\sum P(X=x)=0.06+0.47+0.21+0.12+0.14=1[/tex]

Thus, the probability distribution is valid.

(b)

The histogram is attached below.

(c)

The formula of mean of a discrete probability distribution is:

[tex]\mu=\sum x.P(X=x)[/tex]

Compute the mean as follows:

[tex]\mu=\sum x.P(X=x)\\=1.38+15.989.45+6.725+9.38\\=33.474\\\approx 33.47[/tex]

Thus, the mean is 33.47.