Question

What is the income distribution of super 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. In the following table, income units are in thousands of dollars, and each interval goes up to but does not include the given high value. The midpoints are given to the nearest thousand dollars. Income range 5-15 15-25 25-35 35-45 45-55 55 or more Midpoint x 10 20 30 40 50 60 Percent of super shoppers 20% 14% 21% 17% 18% 10% (a) Using the income midpoints x and the percent of super shoppers, do we have a valid probability distribution? Explain. Yes. The events are distinct and the probabilities do not sum to 1. Yes. The events are indistinct and the probabilities sum to less than 1. No. The events are indistinct and the probabilities sum to more than 1. No. The events are indistinct and the probabilities sum to 1. Yes. The events are distinct and the probabilities sum to 1. (b) Use a histogram to graph the probability distribution of part (a). Maple Generated Plot Maple Generated Plot Maple Generated Plot Maple Generated Plot (c) Compute the expected income μ of a super shopper. (Round your answer to two decimal places.) μ = thousands of dollars (d) Compute the standard deviation σ for the income of super shoppers. (Round your answer to two decimal places.) σ = thousands of dollars

Answer #1

Income range | Midpoint x | Percent of super shoppers | P(x=x) |

5-15 | 10 | 20% | 0.20 |

15-25 | 20 | 14% | 0.14 |

25-35 | 30 | 21% | 0.21 |

35-45 | 40 | 17% | 0.17 |

45-55 | 50 | 18% | 0.18 |

55 or more | 60 | 10% | 0.10 |

sum | 1 |

(a) Using the income midpoints x and the percent of super shoppers, do we have a valid probability distribution?

Ans:Yes. The events are distinct and the probabilities sum to 1.

#Ansb) histogram

c)

µ = 10*0.20+20*0.14+30*0.21+40*0.17+50*0.28+60*0.10 = 32.9

µ =32.9

d)

*σ*=sqrt(∑*x*2⋅*p*(*x*)−*μ*2)

∑*x*2⋅*p*(*x*)=1347

*σ*=sqrt(∑*x*2⋅*p*(*x*)−*μ*2)=sqrt(1347−(32.9)2)=16.27

#σ =16.27

What is the income distribution of super 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. In the
following table, income units are in thousands of dollars, and each
interval goes up to but does not include the given high value. The
midpoints are given to the nearest thousand dollars. Income range
5-15 15-25 25-35 35-45 45-55 55 or more Midpoint x...

What is the income distribution of super 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. In the
following table, income units are in thousands of dollars, and each
interval goes up to but does not include the given high value. The
midpoints are given to the nearest thousand dollars.
Income range
5-15
15-25
25-35
35-45
45-55
55 or more
Midpoint
x...

What is the income distribution of super 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. In the
following table, income units are in thousands of dollars, and each
interval goes up to but does not include the given high value. The
midpoints are given to the nearest thousand dollars.
Income range 5-15 15-25
25-35 35-45 45-55 55 or
more
Midpoint x ...

What is the income distribution of super 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. In the following table, income units are in thousands of
dollars, and each interval goes up to but does not include the
given high value. The midpoints are given to the nearest thousand
dollars.
Income range
5-15
15-25
25-35
35-45
45-55
55 or more
Midpoint
x...

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 over
Midpoint x 23, 34, 45, 56, 67
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For the 62-and-over group, use the midpoint 67 years.
(a) Using the age midpoints x and the percentage of super...

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 over
Midpoint x
23
34
45
56
67
Percent of super
shoppers
10%
43%
20%
10%
17%
For the 62-and-over group, use the midpoint 67 years.
(a) Using the age midpoints x and the percentage of
super...

What is the income distribution of super 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. In the following table, income units are in thousands of
dollars, and each interval goes up to but does not include the
given high value. The midpoints are given to the nearest thousand
dollars.
Income range
5-15 -- 15-25 -- 25-35 -- 35-45 -- 45-55 --...

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 over
Midpoint x
23
34
45
56
67
Percent of super
shoppers
8%
45%
21%
13%
13%
For the 62-and-over group, use the midpoint 67 years.
(a) Compute the standard deviation σ for ages of super
shoppers....

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