Question

Excell Computers promptly shipped two servers to its biggest client. The company profits RM5,000 on each one of these big systems. The shipping worker randomly selected the system without replacement that were delivered from 15 computers in stock. The system contain 4 refurbished computer, with 11 new computers in the warehouse.

If the client gets two new computers, Excell earns RM10,000 profit. If the client gets a refurbished computer, it’s coming back for replacement and Excell must pay the RM400 shipping fee, with leaves RM9,600 profit. If both computers shipped are refurbished, consequently the client will return both and cancel the order. As a result, Excell will be out any profit and left with RM8,000 in shipping cost. Let X be a random variable for the amount of the profit earned on the order.


Construct a probability distribution table and the amount of profit earned for the computer condition. (12 marks)

Calculate the expected profit then interpret the value. (3 marks)​

Answer 1

Answer:

$9215.24

Step-by-step explanation:

Total Number of Computers=15

Number of New=11

Number of Refurbished Computers=4

• P(New)=11/15
• P(Refurbished)=4/15

$P(NN)=\frac{11}{15} \times \frac{10}{14} = \frac{11}{21}\\P(NR)=\frac{11}{15} \times \frac{4}{14} = \frac{22}{105}\\P(RN)=\frac{4}{15} \times \frac{11}{14} = \frac{22}{105}\\P(RR)=\frac{4}{15} \times \frac{3}{14} = \frac{2}{35}$

Let X be the amount of profit earned on the purchase. The probability distribution of X is given as:

$\left|\begin{array}{c|c|c|c|c} Profit(X)& NN=\ 10000 &NR=\ 9600& RR=-\ 800\\ P(X)&\dfrac{11}{21}&\dfrac{44}{105}&\dfrac{2}{35}\end{array}\right|$

(b) Expected Profit

$\text{Expected Profit}=\sum X_iP(X_i)\\=(10000 \times \dfrac{11}{21}) +(9600 \times \dfrac{44}{105}) + (-800 \times \dfrac{2}{35})\\=\ 9215.24$

The store is expected to make an average profit of $9215.24 on the order.

Answer 2

Answer:

Check the probability distribution table and the amount of profit earned is contained in the file attached.

Expected Profit, E(x) = RM9216.8

Explanation:

Probability that 1st computer is refurbished, P₁ = 4/15

Probability that 1st computer is not refurbished, q₁ = 11/15

Probability that 2nd computer is refurbished, P₂ = 3/14

Probability that 2nd computer is not refurbished, q₂ = 11/14

Excel makes a profit of X = RM10,000 if the two computers are new( i.e. none is refurbished)

P(X=RM10000) = q₁q₂ = 4/15 * 3/14

P(X=RM10000) = 0.52

Excel makes a profit of X = RM9600 if just one computer is refurbished

P(X=RM9600) = P₁q₂ + P₂q₁

P(X=RM9600) = (4/15 * 4/14) + (3/14 * 11/15) = 0.419

Excel makes a loss of RM800 ( X = -RM800) if the two computers are refurbished

P(X=-RM800) = P₁P₂

P(X=-RM800) = 4/15 * 3/14

P(X=-RM800) = 0.057

The table that contains the probability distribution and the amount of profit earned is attached as a file below.

2) Expected Profit

E(x) = Σ xP(x)

E(x) = (10000*0.524) + (9600*0.419) - (800 * 0.057)

E(x) = 5240 + 4022.4 - 45.6

E(x) = RM9216.8