Question

company makes electronic gadgets. one out of every 20 gadgets is faulty, but the company
8 profit on the sale of any working gadget, but suffers a loss of $200 for every faulty
adget because they have to repair the unit. what is the expected profit or loss for every
atch of 20 gadgets sold? (round your final answer to two decimal places and select the most
ccurate option from below).
○ an expected loss of $3.85
○ an expected profit of $7.14
○ an expected profit of $1.95
○ an expected loss of $12.48
○ an expected loss of $2.40
○ an expected profit of $5.10
○ an expected loss of $6.52
○ the correct answer is not listed

Explanation:

Step1: Calculate the probability of a faulty and non - faulty gadget

The probability of a faulty gadget \(p_f=\frac{1}{20}=0.05\), and the probability of a non - faulty (working) gadget \(p_w = 1 - p_f=1 - 0.05 = 0.95\)

Step2: Calculate the expected value formula

The expected value \(E(X)\) for a batch of \(n = 20\) gadgets is given by \(E(X)=n\times(p_w\times8+p_f\times(- 200))\)
Substitute \(n = 20\), \(p_w = 0.95\), and \(p_f=0.05\) into the formula:

$$
LATEXBLOCK0
$$

Step3: Calculate the expected value per gadget

The expected value per gadget \(=\frac{-48}{20}=-2.4\)

Answer:

An expected loss of \(\$2.40\)