According to the most recent data, the CDC estimated that the mean height for adult men in the U.S. was 69 inches with a standard deviation of 3 inches. Suppose [tex]X[/tex], height in inches of adult men, follows a normal distribution. Let [tex]x = 72[/tex], the height of a man who is 6' 0" tall. Find and interpret the z-score of the standardized normal random variable.

Select the correct answer below:

A. This means that [tex]x = 72[/tex] is one standard deviation (1σ) above or to the right of the mean, [tex]\mu = 69[/tex].
B. This means that [tex]x = 72[/tex] is two standard deviations (2σ) above or to the right of the mean, [tex]\mu = 69[/tex].
C. This means that [tex]x = 72[/tex] is three standard deviations (3σ) above or to the right of the mean, [tex]\mu = 69[/tex].
D. This means that [tex]x = 72[/tex] is one standard deviation (1σ) below or to the left of the mean, [tex]\mu = 69[/tex].
E. This means that [tex]x = 72[/tex] is two standard deviations (2σ) below or to the left of the mean, [tex]\mu = 69[/tex].
F. This means that [tex]x = 72[/tex] is three standard deviations (3σ) below or to the left of the mean, [tex]\mu = 69[/tex].

The z-score of the standardized normal random variable is 1, and it indicates that the height of this man is above average and higher than most of the adult male population in the U.S.

According to the given question, the mean height for adult men in the U.S. is 69 inches and the standard deviation is 3 inches. We need to find and interpret the z-score of the standardized normal random variable when the height of a man who is 6'0" tall is 72 inches.Let's first define the z-score:It is defined as the number of standard deviations between the observed value of the variable and the mean of the population.

So, the formula for calculating the z-score is given as:z = (x - μ) / σwhere, x is the observed value of the variable, μ is the mean of the population and σ is the standard deviation of the population.Now, we can find the z-score for the given height as follows:z = (x - μ) / σ = (72 - 69) / 3 = 1

The calculated z-score is 1. It tells us that the height of a man who is 6'0" tall (72 inches) is 1 standard deviation above the mean height for adult men in the U.S. (69 inches). It means that the height of this man is higher than 84% of the adult male population in the U.S.

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