Question

For a 4-units class like Statistics, students should spend average of 12 hours studying for the class. A survey was done on students, and the distribution of total study hours per week is bell-shaped with a mean of 14 hours and a standard deviation of 3 hours.

Use the Empirical Rule to answer the following questions.
a) 68% of the students have study hours that are between
___and____
b) What percentage of the students have study hours that are below 23? ___%
i) 11 and 17 hours
ii) 8 and 20 hours
iii) 5 and 23 hours

Answer 1

a) 68% of the students have study hours between 11 and 17 hours. b) The percentage of students with study hours below 23 is 99.7%.

Step-by-step explanation:

a) 68% of the students have study hours that are between 11 and 17 hours

To find the range of study hours that includes 68% of the students, we can use the empirical rule. The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean.

Since the mean study hours is 14 hours and the standard deviation is 3 hours, we can calculate the range as follows:

Lower limit: Mean - 1 standard deviation = 14 - 3 = 11 hours

Upper limit: Mean + 1 standard deviation = 14 + 3 = 17 hours

Therefore, 68% of the students have study hours between 11 and 17 hours.

b) The percentage of students with study hours below 23 is 99.7%.

To find the percentage of students with study hours below 23, we can again use the empirical rule. The empirical rule states that approximately 99.7% of the data falls within three standard deviations of the mean.

Since the mean study hours is 14 hours and the standard deviation is 3 hours, we can calculate the percentage as follows:

Percentage below 23: (Mean + 3 standard deviations) / Total percentage = (14 + 3(3)) / 100 = 23 / 100 = 0.23 or 23%.

Therefore, the correct answer is iii) 5 and 23 hours.