Question

A businessman bought a dealership that is incurring a loss of $500,000 a year. He decided to strategize in order to turn the business around. In addition to the $500,000 annual loss, his fixed cost for running the dealership on a monthly basis is $5,000. The number of cars sold per week and their probabilities mimic the outcomes of three coins being flipped. The number of cars sold in a week was observed to be the same as the number of tails that appear in a three coin flip. See the distribution:


Number of Tails 0 |1 |2 |3
probablity 1/8 | 3/8 | 3/8 | 1/8

Answer 1

What is the expected number of cars sold in one week?


A.

0




B.
1




C.
1.5




D.
2




E.
2.5

Answer 2

@amistre64

Answer 3

okay, you are constructing a weighted average here.

flipping 0 tails is the same as selling 0 cars, and happens with probability 1/8
flipping 1 tail is the same as selling 1 car, and happens with probability 3/8
flipping 2 tails is the same as selling 2 cars, and happens with probability 3/8
flipping 3 tails is the same as selling 3 cars, and happens with probability 1/8

Answer 4

on average, 1/8 of the time no cars will be sold. 3/8 of the time, 1 car will be sold. 3/8 of the time 2 cars will be sold. 1/8 of the time, 3 cards will be sold.

Answer 5

multiply each number of cars sold by its probability, and add them up.

Answer 6

that's the expected value of cars sold in a week.

Answer 7

thinking of it a slightly different way, if you had 8 weeks, 1 week you sell 0 cars. 3 weeks you sell 1 car. 3 weeks you sell 2 cars. 1 week you sell 3 cars. how many cars are sold over those 8 weeks? what is the average number of cars sold per week?

Answer 8

i got 2.25

Answer 9

try again.

Answer 10

show your work

Answer 11

.375 + 1.125+ .75= 2.25

Answer 12

show me how you got those numbers.

Answer 13

1* 3/8= .375, 2*3/8, 3*1/8

Answer 14

I agree that 1*3/8 = 0.375. I don't agree about the others. in any case, there's no need to convert to decimals at this point in the problem, and it's causing you to make mistakes. just do it as fractions.

Answer 15

i get the same things

Answer 16

show me your work.

Answer 17

2 *3 divided by 8, etc.

Answer 18

i dont see what im doing wrong

Answer 19

look, you aren't doing it correctly, why are you resistant to showing me exactly what you did so I can correct you?

Answer 20

yes, you don't, but I will!

Answer 21

thats what i did though

Answer 22

let's go through it again:

0 cars are sold 1/8 of the time
1 car is sold 3/8 of the time
2 cars are sold 3/8 of the time
3 cars are sold 1/8 of the time

\[0*\frac{1}{8} + 1*\frac{3}{8} + 2*\frac{3}{8} + 3*\frac{1}{8} =\]

Answer 23

what does that equal?

Answer 24

1.5

Answer 25

oh i know what i did wrong

Answer 26

yes, 1.5 is correct.

Answer 27

3/8 + 6/8 + 3/8 = 12/8 = 3/2 = 1.5.