To start solving, find the difference between the mean of the data set and the lower bound of the given interval.
97.5 %
Practice makes perfect
We know that the set of data is normally distributed with a mean of 100 and a standard deviation of 10. We will find the probability of choosing a value that is at least 80.
x≥ 80
First, let's find the difference between 80 and the mean 100.
80- 100= - 20
Then, we will divide the difference by the standard deviation 10.
- 20/10=- 2
Thus, 100 is 2 standard deviations below the mean. To find the probability, we will shade the percent of data which is no more than 2 standard deviations below the mean.
Finally, we can find the percent of data by adding the percents of the shaded areas.
