Question

What is the probability that a white referee will call a number of fouls x on a white player that is within 1 standard deviation of the expected value E(x)?

A) Describe the relationship between referee behavior and player ethnicity.
B) Calculate the probability using the standard deviation formula.
C) Explain the significance of standard deviation in this scenario.
D) Compare the probabilities for different standard deviation intervals.

Answer 1

The probability of a referee calling a number of fouls within 1 standard deviation of the expected value is approximately 68.27% if the fouls called follow a normal distribution. To calculate this, the formula 'value = mean + (#ofSTDEVs)(standard deviation)' is used where mean is the expected number of fouls.

Step-by-step explanation:

The student's question pertains to understanding the probability that a referee will call a number of fouls on a player that is within 1 standard deviation of the expected value. Standard deviation is a measure of the amount of variation or dispersion of a set of values.

Probability can be calculated using the properties of the normal distribution. If the fouls called follow a normal distribution, then the probability that an observation falls within 1 standard deviation of the mean is approximately 68.27%. This is because for a normal distribution, about 68.27% of the data falls within 1 standard deviation from the mean.

To calculate the probability using the standard deviation formula, one could utilize the expression: value = mean + (#ofSTDEVs)(standard deviation), where mean is the expected number of fouls and standard deviation is the typical amount by which the actual number of fouls deviates from the mean.