Respuesta :
Answer:
Ron's ERA has a z-score of -2.03.
Karla's ERA has a z-score of -1.86.
Due to the lower z-score, Ron had a better yean than Karla relative to their peers.
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
In this question:
Since the lower the ERA, the better the pitcher, whoever's ERA has the lower z-score had the better year relative to their peers.
Ron
ERA of 3.06, so [tex]X = 3.06[/tex]
For the males, the mean ERA was 5.086 and the standard deviation was 0.998. This means that [tex]\mu = 5.086, \sigma = 0.998[/tex]
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{3.06 - 5.086}{0.998}[/tex]
[tex]Z = -2.03[/tex]
Ron's ERA has a z-score of -2.03.
Karla
ERA of 3.28, so [tex]X = 3.28[/tex]
For the females, the mean ERA was 4.316 and the standard deviation was 0.558. This means that [tex]\mu = 4.316, \sigma = 0.558[/tex]
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{3.28 - 4.316}{0.558}[/tex]
[tex]Z = -1.86[/tex]
Karla's ERA has a z-score of -1.86.
Which player had the better year relative to their peers, Ron or Karla?
Due to the lower z-score, Ron had a better yean than Karla relative to their peers.
