Question

Ana is a dedicated Skee Ball player who always rolls for the 50-point slot. The probability distribution of Ana's score X on a randomly sclected roll of the ball is shown here.

Score 10 20 30 40 50

Probability 0.32 0.27 0.19 0.15 0.07



What is the mean of X? Interpret this value.



A) μY = 23.8. If Anna rolls many, many Skec Balls, the average number of points scored would be about 23.8 points.

B) μY = 30. If Anna rolls many, many Skce Balls, the average number of points scored would be about 30 points.



C) μY - 23.8. If Anna rolls many, many Skee Balls, the total number of points scored would be 23.8 points.



D) The mean cannot be calculated because we do not know the sample size.



E) μY - 30. If Anna rolls many, many Skee Balls, the total number of points scored would be 30 points.

Answer 1

The mean of Ana's score X is 23.8, calculated as the sum of each score multiplied by its probability. The mean represents the average score Ana would achieve over many games.

Step-by-step explanation:

To calculate the mean of Ana's score, denoted as μ (mu), we need to multiply each score by its corresponding probability and then sum up those products. This is the expected value of Ana's score.

μ = (10 × 0.32) + (20 × 0.27) + (30 × 0.19) + (40 × 0.15) + (50 × 0.07)

= 3.2 + 5.4 + 5.7 + 6 + 3.5

= 23.8

So, the mean of X is 23.8. This value represents what Ana's average score would be if she played many, many games of Skee Ball. Therefore, the correct interpretation is option A: If Ana rolls many, many Skee Balls, the average number of points scored would be about 23.8 points.

Answer 2

The mean of X, denoted as μX, represents the average score that Ana is expected to get when playing Skee Ball. To calculate the mean, we multiply each score by its corresponding probability and sum the results.

In this case, we have the following scores and their probabilities:

Score: 10 20 30 40 50

Probability: 0.32 0.27 0.19 0.15 0.07

To calculate the mean, we multiply each score by its probability and sum the results:

Mean = (10 * 0.32) + (20 * 0.27) + (30 * 0.19) + (40 * 0.15) + (50 * 0.07)

Mean = 3.2 + 5.4 + 5.7 + 6 + 3.5

Mean = 23.8

Therefore, the mean of X is 23.8.

Interpreting this value, it means that if Ana rolls many, many Skee Balls, the average number of points she would score per roll would be about 23.8 points. This value represents the expected value or the long-term average score that Ana would achieve when playing Skee Ball.

Therefore, the correct answer is A) μY = 23.8. If Anna rolls many, many Skee Balls, the average number of points scored would be about 23.8 points.

Step-by-step explanation: