Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
The weights of 1,000 men in a certain town follow a normal distribution with a mean of 150 pounds and a standard deviation of 15 pounds.
From the data, we can conclude that the number of men weighing more than 165 pounds is about
, and the number of men weighing less than 135 pounds is about
.

Question

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
The weights of 1,000 men in a certain town follow a normal distribution with a mean of 150 pounds and a standard deviation of 15 pounds.
From the data, we can conclude that the number of men weighing more than 165 pounds is about 
, and the number of men weighing less than 135 pounds is about 
.

Mercury · Answer

z-score formula:

$$z = \frac{ x-μ }{ σ }$$
where z is the z-score, x is the value being examined, μ is the mean, σ is the standard deviation

first, calculate the z-score for x = 165 and then use a calculator/z-table to find the associated probability. this will give you the probability of the weight being < 165 lbs, so to find the probability of > 165 lbs, simply take 1 - (probability weight < 165 lbs). multiply by 1,000 men to get the # of men.

Similar logic with < 135 lbs. calculate the z-score and the associated probability (since we want the probability < 135 lbs you don't have to the 1 - thing this time)