Answer:
a) 95% of the data fall in the range of 20 to 40.
b) 99.7% of the data fall in the range of 15 to 45.
c) 68% of the data fall in the range of 25 to 35.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 30
Standard deviation = 5
a. 20 to 40
20 = 30 - 2*5
So 20 is two standard deviations below the mean
40 = 30 + 2*5
So 40 is two standard deviations above the mean
By the Empircal rule, 95% of the data fall in the range of 20 to 40.
b. 15 to 45
15 = 30 - 3*5
So 15 is three standard deviations below the mean
45 = 30 + 3*5
So 45 is three standard deviations above the mean
By the Empircal rule, 99.7% of the data fall in the range of 15 to 45.
c. 25 to 35
25 = 30 - 1*5
So 25 is one standard deviation below the mean
35 = 30 + 1*5
So 35 is three standard deviation above the mean
By the Empirical rule, 68% of the data fall in the range of 25 to 35.
