The complaints department of a certain supermarket receives

The complaints department of a certain supermarket receives an average of 10 calls per day regarding the service. Assuming that the number of calls is normally distributed with a standard deviation of 5 calls. What is the probability that the call center receives 8 to 12 calls per day?

Solution

Let X denote the number of calls per day

X~N(10,5) where mean is 10 and standard deviation is 5

define Y=(X-10)/5

then Y~N(0,1)

P(7.5<=X<=12.5)=P( (7.5-10)/5 <=Y<= (12.5-10)/5 ) = P(-0.5<=Y<=0.5)

= P(Y<=0.5) - P(Y<= -0.5)

=  0.3829249

=