Start by finding how far the given scores are from the mean.
C
Practice makes perfect
We have been told that in an entry exam, scores are normally distributed with a mean of 140 and a standard deviation of 20. We want to find the probability that a person who took the test scored between 120 and 160. To do so we will find the percentage of the scores that is between 120 and 160.
120 < x < 160
First, let's find the differences between the given scores and the mean 140.
160- 140= 20
140 - 120 = 20
As we can see, both of the scores are 20 units away from the mean. Now, we will express this difference in terms of the standard deviation. To do so, let's divide the difference by the standard deviation, 20.
20/20=1
Thus, 160 is 1 standard deviation above the mean and 120 is 1 standard deviation under the mean. To find the percentage, we will shade the total percent of scores that are between 1 standard deviation above the mean and 1 standard deviation under the mean.
Notice that we have 34 % between 120 and 140, and 34 % between 140 and 160. Last, we will calculate the total percent of the score by adding those percentages.
34 % + 34 % = 68 %
The probability that a person who took the test scored between 120 and 160 is 68 %, which corresponds to option C.
