The average amount of hours a group of people spend working

The average amount of hours a group of people spend working can be estimated through a normal distribution (demonstrated in the below graph)

A. The middle 50% of working hours fall between ____ hours (on low end) and ___ hours (on high end)
B. People who work at least ____ hours are in the top 5% of working hours,

Solution

50% are from x -0.67488 sigma to x+0.67488 sigma

so 6.6 - 1.2*0.67488= 5.79

6.6 + 1.2*0.67488 = 7.41

so 5.79 to 7.41

b)

P(z>c) = 0.05

z = 1.645

so x = 6.6 + 1.645*1.2= 8.574