Question

Suppose that the probabilities of a customer purchasing​ 0, 1, or 2 books at a book store are 0.20.2​, 0.30.3​, and 0.50.5​, respectively. What is the standard deviation of this​ customer's book​ purchases? The standard deviation of the​ customer's book purchases is nothing.

Answer 1

0.78

Explanation:

We have the next probability distribution:

X P(X)

0 0.2

1 0.3

2 0.5

As we can see when we add all the probabilites the result is 1. Now calculating the mean we have:

`mean=\mu=(0*0.2)+(1* 0.3)+(2* 0.5)=0+0.3+1=1.3`

The standard deviation is:

`\sigma=\sqrt{\sum(x-\mu)^(2)(P(x))}`

Then using the data that we have:

`\sigma=\sqrt{\sum(x-\mu)^(2)(P(x))}\\\sigma=\sqrt{(0-1.3)^(2)(0.2)+(1-1.3)^(2)(0.3)+(2-1.3)^(2)(0.5)}\\\\\sigma=\sqrt{(-1.3)^(2)(0.2)+(-0.3)^(2)(0.3)+(0.7)^(2)(0.5)}\\\\\sigma=√((1.69)(0.2)+(0.09)(0.3)+(0.49)(0.5))\\\\\sigma=√(0.338+0.027+0.245)\\\\\sigma=√(0.61)\\\\\sigma=0.78\\`

Then the standard deviation is 0.78