We have been told that the scores on a test are normally distributed with a mean of 16.4 and a standard deviation of 2.6. We will find that the percentage of data is less than 19.
x< 19
First, let's find the difference between 19 and the mean 16.4.
19- 16.4= 2.6
Then, we will divide the difference by the standard deviation 2.6.
2.6/2.6=1
Therefore, 19 is 1 standard deviation above the mean. We can use the Empirical Rule to help us visualize the data with these parameters. To find the percentage, we will shade the percent of data which is no more than 1 standard deviation above the mean.
Finally, we can find the percentage by adding the percentages of the shaded areas.
