The City Manager of Saint Thomas wants to cut down on the amount of \"red tape\"
ID: 2922781 • Letter: T
Question
The City Manager of Saint Thomas wants to cut down on the amount of "red tape" among city departments. As a first step, she collects data on the number of pages of rules and regulations issued by each department (city-wide rules and regulations are not included in this count). The number of pages of rules and regulations across the departments has a normal distribution with a mean of 61.3 and a standard deviation of 11.8. According to these data, what percent of the city departments have issued 70 or more pages of rules and regulations? 80 or more pages? 100 or more pages?
Explanation / Answer
Mean is 61.3 and s is 11.8. z can be found as (x-mean)/s
a) P(x>70)=P(z>(70-61.3)/11.8)=P(z>0.7373) or 1-P(z<0.74)
Thus from normal distribution table we see that it is 1-0.7704=0.2296
b) P(z>80)=P(z>(80-61.3)/11.8)=P(z>1.58) or 1-P(z<1.58)=1-0.9429=0.0571
c) P(z>100)=P(z>(100-61.3)/11.8) =P(z>3.28) , THis is very close to 0