For a sample of 10 patients serum HDL cholesterol readings w

For a sample of 10 patients, serum HDL cholesterol readings were:

70, 56, 48, 48, 53, 36, 49, 28, 35, 68

Use the Empirical Rule to approximate the percentage of patients with serum HDL cholesterol within 2 standard deviations of the mean.
Percent = (whole number)


(d) Use the Empirical Rule to approximate the percent of patients with serum HDL cholesterol between 35.46 and 62.74.
Percent =  (whole number)


(e) Using the Empirical Rule, we would say almost all of the data is between
Lower value  (3 decimal places)
and
Upper value  (3 decimal places)

Solution

For a sample of 10 patients, serum HDL cholesterol readings were:

70, 56, 48, 48, 53, 36, 49, 28, 35, 68

mean =49.10

SD=13.642

The Empirical Rule (68-95-99.7) says that if the population of a statistical data set has a normal distribution

Use the Empirical Rule to approximate the percentage of patients with serum HDL cholesterol within 2 standard deviations of the mean.
Percent = (whole number) =95%


Use the Empirical Rule to approximate the percent of patients with serum HDL cholesterol between 35.46 and 62.74.

35.46= mean-1sd   and 62.74=mean+1sd

About 68% of the values lie within 1 standard deviation of the mean

Percent =  (whole number) =68%


Using the Empirical Rule, we would say almost all of the data is between
Lower value  (3 decimal places)andUpper value  (3 decimal places)

About 99.7% of the values lie within 3 standard deviations of the mean

Lower =49.10 - 3*13.642 = 8.174

upper =49.10 + 3*13.642 = 90.026