Question

Q1. Ten percent of the items produced by a machine are defective. A random sample of 100 items is selected and checked for defects. What is the standard error of the distribution of the sample proportions? Round your answer to three decimal places.

Answer 1

Answer: 0.030

Step-by-step explanation:

Given: The percent of the items produced by a machine are defective  :$P=10\%=0.10$

The percent of the items produced by machine which are not defective:$Q=1-0.1=0.9$

Sample size : n = 100

Now, the standard error of the proportion is given by :-

$\text{S.E.}=\sqrt{\dfrac{0.1\times0.9}{100}}\\\\\Rightarrow\text{S.E.}=0.030$

Hence, the the standard error of the distribution of the sample proportions=0.030