Tony B.is attempting to start a landscaping business.He estimates that to break-even,he will need about 150 customers.He believes that he will lose approximately $500 per customer for each customer fewer than the 150.At the moment,he believes there is an 80% probability that he will be able to secure between 130 and 170 customers,and that there is a 50/50 chance that demand will be greater than 160 customers.What is the mean or expected number of sales?
A)130
B)150
C)160
D)170
E)None of the above

Question

Quizplus · Accepted Answer

The expected value or mean of the number of sales can be calculated using the following formula:

Expected value = (probability of low demand * low demand) + (probability of high demand * high demand)

Plugging in the values given: 
- Probability of low demand (130-150 customers) = 0.8/2 = 0.4 
- Probability of high demand (150-170 customers) = 0.8/2 + 0.5 = 0.9 
- Low demand = 140 customers ((150 customers - 130 customers)/2 + 130 customers) 
- High demand = 165 customers ((170 customers - 150 customers)/2 + 150 customers)

Expected value = (0.4 * 140) + (0.9 * 165) = 144 + 148.5 = 292.5

Since Tony cannot have a fractional number of customers, we round up to the nearest whole number to get the expected number of sales:

Expected number of sales = 293, which is closest to 160 (Choice C).

Tony BIs Attempting to Start a Landscaping Business