About 95 % of the data values fall within 2 standard deviations of the mean.
About 99.7 % of the data values fall within 3 standard deviations of the mean.
We can look at a diagram to better visualize these properties.
Now, we are told that the scores on a test are normally distributed with a mean of 74 and a standard deviation of 8. Using this information we want to find the percentage of juniors whose score is no more than 90.
x≤ 90
First, let's find the difference between 90 and the mean 74.
90- 74= 16
Next, we will divide the difference by the standard deviation 8.
16/8= 2
Therefore, 90 is 2 standard deviations above the mean. Let's draw a normal curve for the given mean and standard deviation. To find the percentage, we will shade the area that represents values no more than 2 standard deviations above the mean.
Finally, we can find the percentage of juniors by adding the percentages of the shaded areas.
