the probability of the number of defective circuit boards in a shipment is given in the tables for two different companies.
company a
company b
what is the expected number of defective circuit boards for company a?
what is the expected number of defective circuit boards for company b?
which company should be chosen for purchasing circuit boards? explain.
a; lowest expected number of defective boards
b; lowest expected number of defective boards
a; highest expected number of defective boards
b; highest expected number of defective boards

Question

Accepted Answer

# Explanation:
## Step1: Calculate expected value for Company A
The formula for expected value $E(X)=\sum_{i}x_{i}P(x_{i})$.
For Company A:
$$
\begin{align*}
E(X_A)&=(0\times0.21)+(1\times0.30)+(2\times0.41)+(3\times0.08)\
&=0 + 0.30+0.82 + 0.24
\end{align*}
$$
## Step2: Calculate expected value for Company B
For Company B:
$$
\begin{align*}
E(X_B)&=(0\times0.18)+(1\times0.32)+(2\times0.28)+(3\times0.22)\
&=0+0.32 + 0.56+0.66
\end{align*}
$$

# Answer:
The expected number of defective circuit boards for company A is $1.36$.
The expected number of defective circuit boards for company B is $1.54$.
Since $1.36<1.54$, company A should be chosen as it has the lowest expected number of defective boards. So the answer for the third part is “A; lowest expected number of defective boards”.

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Question

Explanation:

Step1: Calculate expected value for Company A

Step2: Calculate expected value for Company B

Answer: