Question

question 7
for a 4 - unit class like statistics, students should spend average of 12 hours studying for the class. a survey was done on 21 students, and the distribution of total study hours per week is bell - shaped with a mean of 12 hours and a standard deviation of 2.5 hours.
use the empirical rule to answer the following questions.
a) 68% of the students spend between hours and hours on statistics each week.
b) 95% of the students spend between hours and hours on statistics each week.
c) 99.7% of the students spend between hours and hours on statistics each week.

Explanation:

Step1: 68% range (μ±σ)

Lower: $12 - 2.5 = 9.5$, Upper: $12 + 2.5 = 14.5$

Step2: 95% range (μ±2σ)

Lower: $12 - 2*2.5 = 7$, Upper: $12 + 2*2.5 = 17$

Step3: 99.7% range (μ±3σ)

Lower: $12 - 3*2.5 = 4.5$, Upper: $12 + 3*2.5 = 19.5$

Answer:

a) 9.5 hours and 14.5 hours
b) 7 hours and 17 hours
c) 4.5 hours and 19.5 hours