We have been told that the scores on a test are normally distributed with a mean of 74 and a standard deviation of 3. We will find the probability that a randomly selected test has a score higher than 77.
x> 77
First, let's find the difference between 77 and the mean 74.
77- 74= 3
Then, we will divide the difference by the standard deviation 3.
3/3=1
Therefore, 77 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 more than 1 standard deviation above the mean.
Finally, we can find the probability by adding the percentages of the shaded areas.
