Question

A bookstore sells books for $2. $3, and $5. Let random variable X="amount of money for one book."

Look at the relative-frequency table below representing the amount of money spent on one item and the relative frequencies with which customers purchase them.


If the expected amount of money spent by a customer is $2.54, what is the standard deviation?

Answer 1

1.01410058673

Explanation:

The standard deviation is just the square root of the variance.

One way variance can be defined as is

`E[x^2]-E[x]^2`

Where E[x] is the first moment (or the mean)

E[x²] is the second moment

We are given the first moment as 2.54, so we just need to solve for moment 2. To do this, just do sum(probability * x^2)

E[x²]=.72*2²+.15*3²+.13*5²= 7.48

Thus, the variance is 7.48-2.54²= 1.0284

Which means the standard deviation is √1.0284= 1.01410058673