Answer:
The game's expected value of points for a turn is 71
Step-by-step explanation:
* Lets explain how to solve the problem
- Expected value is the average value of a random variable over a
large number of experiments
- The expected value measures the center of the probability
distribution
- The expected value is the mean of the random variable
* Lets solve the problem
- The game operator designed a simulation using a random number
generator to predict the points would be earned for a turn
∵ The frequency of scoring 50 points is 55
∵ The frequency of scoring 75 points is 32
∵ The frequency of scoring 150 points is 13
∵ The expected value = mean value
∵ Mean value = sum of the total points ÷ total frequency
∵ The sum of the total points = 50(55) + 75(32) + 150(13)
∴ The sum of the total points = 2750 + 2400 + 1950
∴ The sum of the total points = 7100
∵ The total frequency = 55 + 32 + 13
∴ The total frequency = 100
∴ The mean = 7100 ÷ 100 = 71
∵ The total frequency = the total turns
∵ The mean value = the expected value
∴ The expected value = 71 for a turn
* The game's expected value of points for a turn is 71
