Question

Put some air in your tires: Let X represent the number of tires with low air pressure on a randomly chosen car. The probability distribution of X is as follows.

x 0 1 2 3 4
Px 0.2 0.1 0.4 0.2 0.1
Compute the standard deviation σX. Round the answer to at least three decimal places.

Answer 1

The standard deviation cannot be calculated for the given probability distribution.

Step-by-step explanation:

The standard deviation of a probability distribution can be calculated using the formula:

σX = sqrt(Σ(x^2 * Px) - (μX)^2)

where σX is the standard deviation, Σ(x^2 * Px) is the sum of (x^2 * Px) for each value of x, and (μX)^2 is the square of the mean.

Using the given probability distribution, we can calculate:

σX = sqrt((0^2 * 0.2) + (1^2 * 0.1) + (2^2 * 0.4) + (3^2 * 0.2) + (4^2 * 0.1) - (2.2)^2)

σX = sqrt(1.94 - 4.84)

σX = sqrt(-2.9)

Since the variance cannot be negative, the standard deviation is undefined.