Question

The table below represents the probability density function for the random variable X. Find the standard deviation of X.

Round the final answer to two decimal places.

Answer 1

2.15

Explanation:

Here's the filled out table.

x348P(X=x)152525x⋅P(X=x)3585165(x−μ)2P(X=x)1.1520.7842.704

Note that the mean (also called expected value) μ is the sum of the entries in the third column:

μ=35+85+165=5.4

This value is used to compute the values in the fourth column. For example, the first entry is

(3−5.4)2⋅15=1.152