Answer:
a) 0.975
b) 0.16
c) 0.475
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 = 75
Standard deviation = 5
We also have that since the normal distribution is symmetric, 50% of the measures are below the mean and 50% are above.
a. The relative frequency of rates less than 85 using the 68-95-99.7 rule is
85 is two standard deviations above the mean.
So all the 50% below the mean is below 85
And of the 50% above the mean, 95% is less than 85. So
0.5 + 0.95*0.5 = 0.975
b. The relative frequency of rates greater than 80 using the 68-95-99.7 rule is
80 is one standard deviations above the mean.
Of the 50% above the mean, 68% is less than 80. So 100-68 = 32% is more than 80.
0.32*0.5 = 0.16.
c. The relative frequency of rates between 65 and 75 using the 68-95-99.7 rule is
Within the mean and two standard deviations below the mean.
So 95% of 50%
0.95*0.5 = 0.475
