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in 1977, Pistol Pete Maravich led the NBA with 2273 points. In 2006, Kobe Bryant led the NBA with 2832 points. However, there were many differences between basketball in 1977 and basketball in 2006, including the number of teams and possibility of a three-point shot. The mean number of points for the top 110 players in 1977 was 1198 points with a standard deviation of 379 points. The mean nimber of yards for the top 150 players in 2006 was 1123 points with a standard deviation of 433 points. Who had the better performance, Maravich or Bryant? Explain your reasoning.

Sagot :

Using z-scores, it is found that due to the higher z-score, Bryant had the better performance.

Normal Probability Distribution

In a normal distribution 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]

  • It 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, which is the percentile of X.
  • The above bullet point means that higher z-scores mean a better performance.

For Maravich, we have that the parameters are [tex]X = 2273, \mu = 1198, \sigma = 379[/tex], hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2273 - 1198}{379}[/tex]

Z = 2.84.

For Bryant, we have that the parameters are [tex]X = 2832, \mu = 1123, \sigma = 433[/tex], hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2832 - 1123}{433}[/tex]

Z = 3.95.

Due to the higher z-score, Bryant had the better performance.

More can be learned about z-scores at https://brainly.com/question/24663213

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