What is the difference between the height of the tallest man at 92.95" and the mean height of men at 69.6" and a stanard deviation of 2.8?

How many standard deviations is that?
Convert tallest man to a z score
Does tall mans height meet the criterion of being unusual by corresponding to a z score that does not fall between -2 and 2?

Z score is the score in terms of standard deviations.

Z = (score-mean)/SD

Z = (92.95-69.6)/2.8

Solve for Z.

To calculate the difference between the height of the tallest man and the mean height of men, we simply subtract the mean height from the tallest man's height. So, the difference is 92.95" - 69.6" = 23.35".

To calculate how many standard deviations this difference is, we divide the difference by the standard deviation. So, 23.35" / 2.8 = 8.34 standard deviations. This means that the height of the tallest man is 8.34 standard deviations away from the mean height of men.

To convert the tallest man's height to a z-score, we subtract the mean height from the tallest man's height and divide the result by the standard deviation. So, the z-score = (92.95" - 69.6") / 2.8 = 8.34.

To determine if the tall man's height is unusual based on the z-score, we compare it to the range -2 to +2 standard deviations, which corresponds to about 95% of the population in a normal distribution. Since the tall man's z-score of 8.34 is much larger than +2, it falls outside the range of -2 to +2. Therefore, his height is considered unusual based on this criterion.