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Suppose the average player in the NBA is 78 inches tall with
a standard deviation of 2.7 inches, while the average player 10 points
in the WNBA is 69 inches tall, with a standard deviation of 3.2 inches. Who is
relatively taller based on their comparison to their profession, Lebron James
(NBA) at 81 inches or Candace Parker (WNBA) at 76 inches?
A. O LeBron is relatively taller because he has a larger Z-score.
B. O LeBron is relatively taller because he has a smaller z-score.
a
c. O Candace is relatively taller because she has a larger Z-score.
D. O Candace is relatively taller because she has a smaller Z-score.

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.

For the z-score of Lebron's height, we have that: [tex]X = 81, \mu = 78, \sigma = 2.7[/tex], hence:

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

[tex]Z = \frac{81 - 78}{2.7}[/tex]

[tex]Z = 1.11[/tex]

For the z-score of Candace's height, we have that: [tex]X = 76, \mu = 69, \sigma = 3.2[/tex], hence:

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

[tex]Z = \frac{76 - 69}{3.2}[/tex]

[tex]Z = 2.19[/tex]

Due to the higher z-score, Candace is relatively taller, hence option c is correct.

A similar problem is given at https://brainly.com/question/12982818