Question

shelia does quality control for a company that manufactures lawn mower parts. on any given day, she finds the probability distribution for defective parts as shown in the table. using the data from the table, what is the probability of having 2 defective parts in a day? √ 0.04 complete what is the probability that on a given day there, shelia will find defects? done defective parts: x 0 1 2 3 probability: p(x) 0.85 0.10 0.04 0.01

Explanation:

First Sub - Question (Probability of 2 defective parts)

Step1: Identify the relevant row

In the probability distribution table, for the number of defective parts \(X = 2\), we look at the corresponding probability \(P(X)\).

Step2: Read the probability value

From the table, when \(X = 2\), the probability \(P(X)=0.04\).

Second Sub - Question (Probability of finding defects)

Step1: Understand the event

"Finding defects" means the number of defective parts \(X\geq1\) (i.e., \(X = 1\), \(X = 2\), or \(X = 3\)).

Step2: Sum the relevant probabilities

We know that \(P(X = 1)=0.10\), \(P(X = 2)=0.04\), and \(P(X = 3)=0.01\). The probability of \(X\geq1\) is \(P(X = 1)+P(X = 2)+P(X = 3)\).
\[P(X\geq1)=0.10 + 0.04+0.01=0.15\]
(Alternatively, we can use the complement rule: \(P(X\geq1)=1 - P(X = 0)\). Since \(P(X = 0)=0.85\), then \(1 - 0.85 = 0.15\))

Answer:

0.04