using probability to make decisions\nthe probability of the number of defective circuit boards in a shipment…

using probability to make decisions\nthe probability of the number of defective circuit boards in a shipment is given in the tables for two different companies.\ncompany a\n# defective (x) 0 1 2 3\np(xi) 0.21 0.30 0.41 0.08\ncompany b\n# defective (x) 0 1 2 3\np(xi) 0.18 0.32 0.28 0.22\nwhat is the expected number of defective circuit boards for company a?\nwhat is the expected number of defective circuit boards for company b?\nwhich company should be chosen for purchasing circuit boards? explain.

using probability to make decisions\nthe probability of the number of defective circuit boards in a shipment is given in the tables for two different companies.\ncompany a\n# defective (x) 0 1 2 3\np(xi) 0.21 0.30 0.41 0.08\ncompany b\n# defective (x) 0 1 2 3\np(xi) 0.18 0.32 0.28 0.22\nwhat is the expected number of defective circuit boards for company a?\nwhat is the expected number of defective circuit boards for company b?\nwhich company should be chosen for purchasing circuit boards? explain.

Answer

Explanation:

Step1: Recall expected - value formula

The expected - value formula for a discrete random variable is $E(X)=\sum_{i}x_{i}P(x_{i})$.

Step2: Calculate expected number for company A

$E(X_A)=0\times0.21 + 1\times0.30+2\times0.41 + 3\times0.08$ $=0 + 0.30+0.82 + 0.24$ $=1.36$.

Step3: Calculate expected number for company B

$E(X_B)=0\times0.18 + 1\times0.32+2\times0.28 + 3\times0.22$ $=0 + 0.32+0.56 + 0.66$ $=1.54$.

Step4: Compare expected values

Since $E(X_A)=1.36$ and $E(X_B)=1.54$, and we want to minimize the number of defective circuit - boards, company A should be chosen as it has a lower expected number of defective circuit - boards.

Answer:

What is the expected number of defective circuit boards for company A? 1.36 What is the expected number of defective circuit boards for company B? 1.54 Which company should be chosen for purchasing circuit boards? Explain. Company A, because it has a lower expected number of defective circuit boards (1.36 compared to 1.54 for company B).