Question

The manager of a bookstore recorded the number of customers who arrive at a checkout counter every 5 minutes and calculated the following distribution. Calculate the mean and standard deviation of the random variable.

X P(X)
0 0.10
1 0.20
2 0.25
3 0.25
4 0.20

Answer 1

The mean of the distribution is 2.3 and the standard deviation is 1.14.

Step-by-step explanation:

To calculate the mean of a distribution, we multiply each value by its corresponding probability and sum them up.

So, mean = 0(0.1) + 1(0.2) + 2(0.25) + 3(0.25) + 4(0.2) = 2.3

To calculate the standard deviation, we first calculate the deviation of each value from the mean, square it, multiply by the probability, and sum them up.

So, standard deviation = sqrt[(0-2.3)^2(0.1) + (1-2.3)^2(0.2) + (2-2.3)^2(0.25) + (3-2.3)^2(0.25) + (4-2.3)^2(0.2)] = 1.14