select the correct answer.\nthe height of males approximates a normal distribution. the average height of…

select the correct answer.\nthe height of males approximates a normal distribution. the average height of the players on an nba team is 6.6 feet with a standard deviation of 0.2 feet. if one of the players is 7.5 feet tall, how many standard deviations away from the mean is this players height?\na. 4.5 standard deviations below the mean\nb. 0.9 standard deviations below the mean\nc. 0.9 standard deviations above the mean\nd. 4.5 standard deviations above the mean

select the correct answer.\nthe height of males approximates a normal distribution. the average height of the players on an nba team is 6.6 feet with a standard deviation of 0.2 feet. if one of the players is 7.5 feet tall, how many standard deviations away from the mean is this players height?\na. 4.5 standard deviations below the mean\nb. 0.9 standard deviations below the mean\nc. 0.9 standard deviations above the mean\nd. 4.5 standard deviations above the mean

Answer

Explanation:

Step1: Recall z - score formula

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x$ is the data - point, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step2: Identify values

We are given that $\mu = 6.6$ (mean height), $\sigma=0.2$ (standard deviation), and $x = 7.5$ (player's height).

Step3: Calculate z - score

Substitute the values into the formula: $z=\frac{7.5 - 6.6}{0.2}=\frac{0.9}{0.2}=4.5$. Since the z - score is positive, the player's height is above the mean.

Answer:

D. 4.5 standard deviations above the mean