Answer:
0.281 = 28.1% probability a given player averaged less than 190.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
A bowling leagues mean score is 197 with a standard deviation of 12.
This means that [tex]\mu = 197, \sigma = 12[/tex]
What is the probability a given player averaged less than 190?
This is the p-value of Z when X = 190.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{190 - 197}{12}[/tex]
[tex]Z = -0.58[/tex]
[tex]Z = -0.58[/tex] has a p-value of 0.281.
0.281 = 28.1% probability a given player averaged less than 190.
