Question

A successful basketball player has a height of 6 feet 5 inches, or 196 cm. Based on statistics from a data set, his height converts to the z score of 3.02. How many
standard deviations is his height above the mean?

The player's height is standard deviation(s) above the mean.

(Round to two decimal places as needed.)

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Answer 1

Answer:

The player's height is 3.02 standard deviations above the mean.

Step-by-step explanation:

Consider a random variable X following a Normal distribution with parameter μ and σ.

The procedure of standardization transforms individual scores to standard scores for which we know the percentiles (if the data are normally distributed).  

Standardization does this by transforming individual scores from different normal distributions to a common normal distribution with a known mean, standard deviation, and percentiles.

A standardized score is the number of standard deviations an observation or data point is above or below the mean.

The standard score of the random variable X is:

$Z=\frac{X-\mu}{\sigma}$

These standard scores are also known as z-scores and they follow a Standard normal distribution, i.e. N (0, 1).

It is provided that the height of a successful basketball player is 196 cm.

The standard value of this height is, z = 3.02.

The z-score of 3.02 implies that the player's height is 3.02 standard deviations above the mean.