1. Many textbooks
state that a value that falls more than 1.5 interquartile ranges above
the upper quartile or 1.5 interquartile ranges below the lower quartile
is an "outlier". What percent of the values in a normal distribution
are considered "outliers" using this definition?
2. Imagine two outstanding students who have excelled in academics,
service, and athletics. Anita earned 620 on the SAT verbal and Bonita
scored 27 on the ACT. In other respects, their high school records are
comparable. You learn that the average SAT verbal score is 500, with
standard deviation of 100 points while the ACT has a mean of 18 with a
standard deviation of 6. If we assume that scores on these exams are
approximately normal, can you use thier scores to determine who wins
3. Anita scored at the 60th percentile on a midterm exam while Bonita
scores at the 85th percentile. If we know that the midterm had a mean
of 70 and standard deviation of 10 points, how many points separate
Anita and Bonita on this exam?
4. National Fruit Company claims that the weights of their forty
pound boxes of imported bananas are approximately normal with mean 41
pounds and standard deviation of 4 ounces. How often will a box of
bananas be underweight?
5. For women athletes at UCLA, 62.5 inches is the 25th percentile
height and 65.5 inches is the 75th percentile height.
a) If we assume that heights for women athletes are approximately
normal, find the mean and standard deviation of the distribution of
b) Use the calculations to determine the 90th percentile height for
women athletes at UCLA.
Check your answers.