Question

barbara is a quality control inspector at a shoe factory. at the end of each day, she checks the

Barbara is a quality control inspector at a shoe factory. At the end of each day, she checks the number of imperfections found in sneakers. The table below represents the probability density function for the random variable X, t imperfections found in sneakers per day. Find the standard deviation of X. Round the final answer to two decimal places. x P(X x) 1/4 1/4 1/4 1/4 ecopy toboarDoamioad csw Provide your answer below:

Answer 1

Solution:

Given: Barbara is a quality control inspector at a shoe factory. At the end of each day, she checks the number of imperfections found in a sneakers.

We are given following table in which X : The number of imperfections found in sneakers per day.

x	P(X=x)
0	1/4
2	1/4
4	1/4
7	1/4

We have to find the standard deviation of X.

Formula:

$std = \sqrt{\sum x^{2} \times P(x)-(\sum x \times P(x))^{2}}$

Thus we need to make following table:

x	P(X=x)	x*P(x)	x^2*P(x)
0	1/4	0	0
2	1/4	0.5	1
4	1/4	1	4
7	1/4	1.75	12.25
		r × P(z) 3.25	2.2 x P(r) = 17.25

Thus we get:

$std = \sqrt{\sum x^{2} \times P(x)-(\sum x \times P(x))^{2}}$

std- /17.25 - (3.25)

std= ν/ 17.25-10.5625

std = V 6.6875

sta2,5860

std2,59

Thus the standard deviation of X is :

std2,59