# Probability

*label*Mathematics

*timer*Asked: Jan 13th, 2018

*account_balance_wallet*$20

### Question Description

*In the book Essentials of Marketing Research, William R. Dillon, Thomas J. Madden, and Neil H. Firtle present the results of a concept study for a new wine cooler. Three hundred consumers between 21 and 49 years old were randomly selected. After sampling the new beverage, each was asked to rate the appeal of the phrase: "Not sweet like wine coolers, not filling like beer, and more refreshing than wine or mixed drinks" as it relates to the new wine cooler. The rating was made on a scale from 1 5o 5, with 5 representing "extremely appealing" and with 1 representing "not at all appealing". The data is presented in the attached Excel work sheet. *

You decide that the best way to respond to your management's request is to analyze the following. Please calculate the items below, responding to the prompts.

2. Estimate the probability that a randomly selected 21 to 49 year old consumer

- Would give the phrase a rating of 5
- Would give the phrase a rating of 3 or higher
- Is in the 21-24 age group
- Is a male who gives the phrase a rating of 4
- Is a 35 to 49 year old who gives the phrase a rating of 2 or lower

3. You have data which shows how many cartons of the wine cooler were bought per customer in a month.

- Explain what a probability distribution is then create one using data provided to you.
- What is the mean and the standard deviation of your probability distribution?

4. Your surveys suggest that 30% of the people who heard a test advertisement for the wine cooler would go to the store and buy some to try it. Suppose that six customers enter the store and that they make independent purchase decisions.

- Let x = the number of the six customers who will make a purchase decision. Write the binomial formula for this situation.
- Create a binomial distribution.
- Using the values from the binomial distribution

*The probability that exactly five customers purchase the wine cooler.

*The probability that at no more than four customers purchase the wine cooler.

*The probability that two or fewer customers purchase the wine cooler.

*The probability that at least one customer purchases the wine cooler.

Rating of the appeal of the phrase as it relates to the new wine cooler | Total Sample | Gender | Age | |||

Male | Female | 21 - 24 | 25 -34 | 35-49 | ||

Extremely appealing (5) | 141 | 70 | 83 | 48 | 53 | 40 |

Somewhat appealing (4) | 96 | 49 | 35 | 36 | 32 | 28 |

Neither appealing nor not appealing (3) | 41 | 21 | 20 | 14 | 16 | 11 |

Somewhat unappealing (2) | 13 | 7 | 6 | 4 | 6 | 3 |

Not at all appealing (1) | 9 | 3 | 6 | 4 | 3 | 2 |

QUANTITY PURCHASED PER PERSON IN ONE MONTH | |||

# of six packs purchased | # people who purchased this amount | ||

0 | 3 | ||

1 | 7 | ||

2 | 7 | ||

3 | 12 | ||

4 | 15 | ||

5 | 11 | ||

6 | 10 | ||

7 | 7 | ||

8 | 5 | ||

9 | 5 | ||

10 | 3 |

## Tutor Answer

Here is my answer :)

Probability Question

In the book Essentials of Marketing Research, William R. Dillon, Thomas J. Madden, and Neil H. Firtle

present the results of a concept study for a new wine cooler. Three hundred consumers between

21 and 49 years old were randomly selected. After sampling the new beverage, each was asked to

rate the appeal of the phrase: “Not sweet like wine coolers, not filling like beer, and more refreshing

than wine or mixed drinks” as it relates to the new wine cooler. The rating was made on a scale from

1 to 5, with 5 representing “extremely appealing” and with 1 representing “not at all appealing”.

The data is presented in the attached Excel work sheet.

You decide that the best way to respond to your management’s request is to analyze the following.

Please calculate the items below, responding to the prompts.

Gender

Rating of the appeal of the phrase as it

relates to the new wine cooler

Extremely appealing (5)

Somewhat appealing (4)

Neither appealing nor not appealing (3)

Somewhat unappealing (2)

Not at all appealing (1)

Total

Sample

141

96

41

13

9

Age

Male

Female

21-24

25-34

35-49

70

49

21

7

3

83

35

20

6

6

48

36

14

4

4

53

32

16

6

3

40

28

11

3

2

1. Estimate the probability that a randomly selected 21 to 49 year old consumer

a. Would give the phrase a rating of 5

141

= 0.470

300

b. Would give the rating of 3 or higher

41 + 96 + 141

= 0.927

300

c. Is in the 21-24 age group

48 + 36 + 14 + 4 + 4

= 0.353

300

d. Is a male who gives the phrase a rating of 4

49

= 0.163

300

e. Is a 35 to 49 year old who gives the phrase a rating of 2 or lower

3+2

= 0.017

300

2. You have data which shows how many cartons of the wine cooler were bought per

costumer in a month.

QUANTITY PURCHASED PER PERSON IN ONE MONTH

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