To start solving, find the difference between the mean of the data set, and the lower and upper bounds of the given interval.
99.7 %
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 70 and 130.
70 ≤ x≤ 130
First, let's find the difference between 70 and the mean 100.
70- 100= - 30Now, let's find the difference, between 130 and the mean 100.
130- 100= 30
Then, we will divide the differences by the standard deviation 10.
- 30/10=- 3and30/10=3
Thus, 70 is 3 standard deviations below the mean and 130 is 3 standard deviations above the mean. To find the probability, we will shade the percent of data which is at most 3 standard deviations below the mean and no more than 3 standard deviations above the mean.
Finally, we can find the percent of data by adding the percents of the shaded areas.
