Question

Fifteen items or less: The number of customers in line at a supermarket express checkout counter is a random variable with the following probabilitydistribution.x0 12 34P(x) 0.100.20 0.30 0.20 0.15 0.05Send data to ExcelPart: 0/3Part 1 of 3(a) Compute the mean Hx. Round the answer to two decimal places.(b) compute the standard deviationHx²

Answer 1

mean = 2.25

standard deviation = 1.34

Step-by-step explanation:

The mean of the distribution can be calculated as the sum of each value of x times P(x), so taking into account the table, we get that the mean is equal to

mean = 0(0.10) + 1(0.20) + 2(0.30) + 3(0.20) + 4(0.15) + 5(0.05)

mean = 0 + 0.2 + 0.6 + 0.6 + 0.6 + 0.25

mean = 2.25

Therefore, the mean is 2.25

On the other hand, the variance is equal to the square of the difference between each value and the mean multiplied by its probability, so

variance = (0 - 2.25)²(0.10) + (1 - 2.25)²(0.20) + (2 - 2.25)²(0.30)

+ (3 - 2.25)²(0.20) + (4 - 2.25)²(0.15) + (5 - 2.25)²(0.05)

variance = 0.51 + 0.31 + 0.02 + 0.11 + 0.46 + 0.38

variance = 1.79

Then, the standard deviation is equal to the square root of the variance, so

standard deviation = √1.79

standard deviation = 1.34

Therefore, the standard deviation is 1.34