Question

Let y = the number of siblings for a student at a local high school. Suppose we choose someone from the school at random. The probability distribution of y is as follows.

y 0 1 2 3 4 5
Probability 0.02 0.25 0.35 0.20 0.10 0.08


Calculate the standard deviation of Y. Accurate to 4 decimal places.

Answer 1

The standard deviation of Y is 1.2278.

Step-by-step explanation:

To calculate the standard deviation of Y, we need to calculate the mean of Y first.

The formula for the mean is:

Mean = (y1 * P(y1)) + (y2 * P(y2)) + (y3 * P(y3)) + (y4 * P(y4)) + (y5 * P(y5)) + (y6 * P(y6))

Mean = (0 * 0.02) + (1 * 0.25) + (2 * 0.35) + (3 * 0.20) + (4 * 0.10) + (5 * 0.08)

Mean = 2.31

Next, we calculate the variance using the formula:

Variance = [(y1 - Mean)^2 * P(y1)] + [(y2 - Mean)^2 * P(y2)] + [(y3 - Mean)^2 * P(y3)] + [(y4 - Mean)^2 * P(y4)] + [(y5 - Mean)^2 * P(y5)] + [(y6 - Mean)^2 * P(y6)]

Variance = [(0 - 2.31)^2 * 0.02] + [(1 - 2.31)^2 * 0.25] + [(2 - 2.31)^2 * 0.35] + [(3 - 2.31)^2 * 0.20] + [(4 - 2.31)^2 * 0.10] + [(5 - 2.31)^2 * 0.08]

Variance = 1.5087

Finally, we calculate the standard deviation using the formula:

Standard Deviation = √Variance

Standard Deviation = √1.5087

Standard Deviation ≈ 1.2278