By using Microsoft Excel\'s Analytic Solver Platform to solve the question below

Question

By using Microsoft Excel's Analytic Solver Platform to solve the question below:

An organization is performing a door-to-door marketing campaign to sell goods to consumers. They will visit 30 homes. Consultants estimated they expect to find someone home 80% of the time. When someone is home 65% it is a female. 30% of females make a purchase, and when they make a purchase it is normally distributed with a mean of $22 and a standard deviation of $5. 20% of males make a purcahse, and when they do it is normall distributed with a mean of $28 and a standard deviation of $3.

1.) What is the total amount they can expect to generate in revenues from these 30 visits?

2.) What is the standard deviation of total revenues over 30 visits?

3.) What is the probability they will make more than 100?

Explanation / Answer

(1) Total number of home visited = 30

Expected number of homes where they will find someone = 30 * 0.8 = 24

Expected number of females in these home = 24 * 65/100 = 15.6

Expected number of males in these homes = 24 * 35/100 = 8.4

Out of these females, number of females who will purchase something = 15.6 * 30/100 = 4.68

Out of these males, number of males who will purchase something = 8.4 * 20/100 = 1.68

total amount they can expect to generate in revenues from 30 visits from females = 4.68 * mean female purchase = 4.68 * 22 = $102.96

total amount they can expect to generate in revenues from 30 visits from males = 1.68 * mean male purchase = 1.68 * 28 = $ 47.04

so the total amount they can expect to generate in revenues from these 30 visits = 102.96 + 47.04 = $150

(b) Standard deviation of total revenues

We can calculate it by using variance formula of multiplication

Var(aX + bY) = a2 Var(X) + b2 Var (Y)

Here Var (Females) = 52 = 25 and Var(Males) = 32 = 9

Total revenue = 4.68 * Purchase (Females) + 1.68 * Purchase (Males)

Var(Total revenue) = 4.682 * 25 + 1.682 * 9 = 572.9616

Standard deviation (Total Revenue ) = sqrt (variance) = $23.94

(3) Here we have to find the probability of Total revenue greater than $ 100

so Pr( TR > 100) where mean revenue = $ 150 and std. dev (revenue) = $23.94

so Z - value = ( 100 - 150)/ 23.94 = -2.09

so Pr( TR > 100) = 1 - (-2.09) = 1 - 0.0183 = 0.9817

Related Questions

Navigate

• Browse (All)
• Browse B
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.