To start solving, find the difference between the mean of the data set, and the lower and upper bounds of the given interval.
47.5 %
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 between 80 and 100.
80 ≤ x≤ 100
First, let's find the difference between 80 and the mean 100.
80- 100= - 20
Now, let's find the difference between 100 and the mean 100.
100- 100= 0
Then, we will divide the differences by the standard deviation 10.
- 20/10=- 2and0/10=
Thus, 80 is 2 standard deviations below the mean and 100 is standard deviations from the mean. To find the probability, we will shade the percent of data which is at most 2 standard deviations below the mean and at most equal to the mean.
Finally, we can find the percent of the data by adding the percents of the shaded areas.
