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Jim decides to start a small nonprofit business of renting out motor scooters to help out his area residents. He puts in his own money and buys 5 motor scooters, each priced at $3,000. He incurs no other costs because he keeps the motor scooters in his own garage. The motor scooters last for 5 years. The number of motor scooters and the probability that they would be rented per month is shown in the table.

Number of Scooters 0         1          2           3            4       5

Probability              1/32     5/32     10/32     10/32     5/32    1/32

At what price per month should Jim rent out a scooter in order to break even?

A50

B)150

C)200

D)250

E)300

Verified Answer :

E(x) = [(0)(1/32)+(1)(5/32)+(2)(10/32)+(3)(10/3... ] = 2.53

Answer: Hence, price per month that Jim should rent out a scooter in order to break even = $100 per month.

Step-by-step explanation:

Since we have given that

Number of Scooters 0         1          2           3            4       5

Probability                    1/32     5/32     10/32     10/32     5/32    1/32

So, Expected value would be

\(E[x]=0\times \dfrac{1}{32}+1\times \dfrac{5}{32}+2\times \dfrac{10}{32}+3\times \dfrac{10}{32}+4\times \dfrac{5}{32}+5\times \dfrac{1}{32}\\\\E[x]=2.5\)

Number of years = 5

Number of months = 12

Total months = \(12\times 5=60\ months\)

So, Number of motors in five years according to expected value is given by

\(2.5\times 60=150\)

Number of motor scooters = 5

Cost of each scooter = $3000

So, total cost would be

\(3000\times 5\\\\=\$15000\)

Hence, price per month that Jim should rent out a scooter in order to break even is given by

\(\dfrac{15000}{150}=\$100\)

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