Question

A manufacturer produces widgets that are packaged in boxes of 100. The probability of a widget being defective is 0.021. Find the mean and standard deviation for the number of defective widgets in a box.

Answer 1

Answer:

$\=x=2.1$

$\sigma=2.03$

Step-by-step explanation:

From the question we are told that:

Sample size$n=100$

Probability of  a defective widget $P=0.021$

Generally the equation for binomial trial is mathematically given by

 $q=1-p$

 $q=1-0.021$

 $q=0.979$

Since X is binomial random variable with functions of n and p,The equation of mean \=x

 $\=x=E(x)$

  Where

  $E(x=n*p)$

 $\=x=100*0.021$

 $\=x=2.1$

Generally the equation for variance \sigma is mathematically given by

 $\sigma=\sqrt{nqp}$

 $\sigma=\sqrt{200*0.021*0.979}$

 $\sigma=2.03$