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

Answer:

0.78

Step-by-step 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:

$mean=\mu=(0\times0.2)+(1\times 0.3)+(2\times 0.5)=0+0.3+1=1.3$

The standard deviation is:

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

Then using the data that we have:

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

Then the standard deviation is 0.78