Find the difference between the mean height and the given height in terms of standard deviations.
95 %
Practice makes perfect
We have been told that the heights of adult males are normally distributed with a mean of 72 inches and a standard deviation of 2 inches. We will find the percentage of men who are between 68 and 76inches tall.
68inches ≤ x≤ 76inches
First, let's find the difference between 68inches and the mean.
72inches- 68inches=4Then, we will divide the difference by the standard deviation.
4 inches/2inches=2
Therefore, 68inches is 2 standard deviations below the mean.
Next, let's find the difference between 76 inches and the mean.
76 inches- 72 inches= 4 inches
Again, we will divide the difference by the standard deviation.
4 inches/2 inches=2
Thus, 76 inches is 2 standard deviations above the mean.
To find the probability, we will shade the data that is no more than 2 standard deviations below the mean and no more than 2 standard deviations above the mean.
Finally, we can find the probability that a randomly chosen man is between 68 and 76 inches tall by adding the percentage of data in the shaded regions.
