Answer:
a) 68% of the observations lie between 90 and 150.
b) 95% of the observations lie between 60 and 180.
c) 99.7% of the observations lie between 30 and 210.
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:
Standard deviation = 120
Mean = 30
a. 90 and 150
This is within 1 standard deviation of the mean.
By the Empirical Rule, 68% of the observations lie between 90 and 150.
b. 60 and 180
This is within 2 standard deviations of the mean.
By the Empirical Rule, 95% of the observations lie between 60 and 180.
c. 30 and 210
This is within 3 standard deviations of the mean.
By the Empirical Rule, 99.7% of the observations lie between 30 and 210.
