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

Question

Quizplus · Accepted Answer

To find the expected number of sales, we need to take into account the probabilities of different scenarios.
According to the information given:
- There is an 80% probability that Tony will secure between 130 and 170 customers. This means there is a 10% probability of getting 130, 40% probability of getting 150, and 30% probability of getting 160 or 170 (since the range between 130 and 170 is evenly distributed).
- There is a 50/50 chance that demand will be greater than 160 customers. This means there is a 25% probability of getting each of the values 130, 150, 160, and 170.

To calculate the expected number of sales, we multiply each possible outcome by its probability, and then sum the results:
Expected number of sales = (0.1 x 130) + (0.4 x 150) + (0.3 x 160) + (0.2 x 170)
Expected number of sales = 13 + 60 + 48 + 34
Expected number of sales = 155

Therefore, the best choice is C (160) which is closest to the expected number of sales.

Tony BIs Attempting to Start a Landscaping Business