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Exercises
1. What is the probability that a z-score will lie between 2 and 3?
2. How likely is it for a z-score to be over 2.5?
3. What is the chance that a z-score is less than 1.3?
4. The heights in inches at a certain age are normally distributed with mean 48 and standard
deviation 3.2. What is the probability that a person at that age is over 53 inches tall?
5. The pH (a measurement of acidity) in a lake is normally distributed with mean 6.8 and
standard deviation 0.43. What is the probability that a measurement of pH will be less than
6.6?
6. Daily high temperatures (in degrees Fahrenheit) in a given city in June are normally
distributed with mean 65 and standard deviation 4.5. What is the probability that on a given
June day the high temperature will be between 66 and 70?
7. What z-score is at the 80th percentile?
8. Assume that the average GPA at a college is 3.1 with standard deviation 0.3. How large a
GPA would a student need to have to be in the top 15% of her/his class?
Solutions
1. normalcdf(2, 3, 0,1) = 0.0214 = 2.14%.
2. normalcdf(2.5, 1E99, 0, 1) = 0.00062 = 0.62%.
3. normalcdf (-E99, 1.3, 0, 1) = 0.9032 = 90.32%.
4. normalcdf(53, 1E99, 48, 3.2) = 5.91%.
5. normalcdf(-1E99, 6.6, 6.8, 0.43) = 0.3209 = 32.09%.
6. normalcdf(66, 70, 65, 4.5) = 0.2788 = 27.88%.
7. invnorm(.8, 0, 1) = .84 = 84%.
8. invnorm(.85, 3.1, .3) = 3.41.
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