Question

Skee Ball Ana is a dedicated Skee Ball player (see photo in Exercise 4) who always rolls for the 50-point slot. The probability distribution of Ana’s score X on a randomly selected roll of the ball is shown here. From Exercise 8, μX=23.8 . Calculate and interpret the standard deviation of X.

Short answer

The standard deviation is$\sigma =12.6317$.

Step-by-step solution

Step 1. Given information.

The given information is:

Step 2. Find and interpret the standard deviation of X.

The given mean is 23.8.

The predicted value of the squared departure from the mean is known as the variance:

$$\begin{gathered} {\sigma }^2=\sum {\left(x-\mu \right)}^{2}P\left(x\right) \\ ={\left(10-23.8\right)}^2\times \left(0.32\right)+{\left(20-23.8\right)}^2\times \left(0.27\right)+{\left(30-23.8\right)}^2\times \left(0.19\right)+ \\ {\left(40-23.8\right)}^2\times \left(0.15\right)+{\left(50-23.8\right)}^2\times \left(0.07\right) \\ =159.56 \end{gathered}$$

The standard deviation is:

$$\begin{gathered} \sigma =\sqrt{{\sigma }^2} \\ =\sqrt{159.56} \\ \approx 12.6317 \end{gathered}$$

The average score on a randomly chosen roll of the ball is 12.6317 points higher than the mean score of 23.8.