What is the difference between the height of the tallest man at 92.95" and the mean height of me 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?
To find the difference between the height of the tallest man and the mean height of yourself, you need to subtract the mean height from the tallest man's height.
Height difference = Tallest man's height - Your height mean
Height difference = 92.95" - 69.6" = 23.35"
Now, to find how many standard deviations this height difference is, you need to divide the height difference by the standard deviation of your height.
Number of standard deviations = Height difference / Standard deviation of your height
Number of standard deviations = 23.35" / 2.8 = 8.34
Therefore, the height difference between the tallest man and yourself is approximately 8.34 standard deviations.
To convert the tallest man's height to a z-score, you can use the formula:
z-score = (x - mean) / standard deviation
Where x is the value (in this case, the tallest man's height), mean is the mean height (69.6"), and standard deviation is the standard deviation of your height (2.8").
Z-score = (92.95" - 69.6") / 2.8 = 8.32
So, the tallest man's height corresponds to a z-score of approximately 8.32.
To determine if the tallest man's height is unusual, we compare the z-score to the range of -2 to 2, which is typically considered as the normal range.
Since the z-score is 8.32, which is well outside the range of -2 to 2, we can conclude that the tall man's height is indeed unusual according to the criterion of falling within that range.