The mean length of angelfish (a popular tropical fish for aquariums) is 11.4 cm with a standard deviation of 1.5 cm. Assuming that the length of angelfish is a normal random variable, find the probability that a randomly selected angelfish would be between 12.015 and 15.33 cm in length.

First find the standard deviation values for 12.015 and 15.33:

(12.015-11.4)/1.5=.41

(15.33-11.4)/1.5=2.62

Then use Excel to find percentage of each area up to that point:

normsdist(.41)=.6591

normsdist(2.62)=.9956

Then P(12.015<=X<=15.33)=P(X<=15.33)-P(X<12.015)=.9956-.6591=.3365