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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

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.
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1 Answer

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