# Defects of bottle selection

• Feb 25th 2011, 01:15 PM
dwsmith
Defects of bottle selection
Approximately 10% of the glass bottles coming off a production line have serious defects in the glass. Two bottles are randomly selected for inspection. Find the expected value and the variance of the number of inspected bottles with serious defects.

$p=.10, \ \ \bar{p}=.90$

I am not sure how you use this information to find the expected value.
• Feb 25th 2011, 01:37 PM
harish21
when two bottles are randomly selected, there may be either no bottles with serious defect, or there may be one bottle with serious defect, or there may be both bottles with serious defect.

You can use binomial distribution to find P(X=0), P(X=1), and P(X=2), and then calculate the mean and variance
• Feb 25th 2011, 01:46 PM
pickslides
Quote:

Originally Posted by dwsmith
Approximately 10% of the glass bottles coming off a production line have serious defects in the glass. Two bottles are randomly selected for inspection. Find the expected value and the variance of the number of inspected bottles with serious defects.

$p=.10, \ \ \bar{p}=.90$

I am not sure how you use this information to find the expected value.

$\displaystyle n= 2, p= 0.1$

$\displaystyle E(X) = n\times p , Var(X) = np(1-p)$