The Normal Curve
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Practice Problems1. 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 the scholarship?
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 heights.
b) Use the calculations to determine the 90th percentile height for women athletes at UCLA.