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Classwork Ch. 4.4
AP STATS
Normal Distributions/ Empirical Rule
1. The height of young American women has an approximately normal distribution with mean µ= 65.5
inches and standard deviation σ= 2.5 inches. Find the relative frequencies (proportion) of each of the
following:
A. a woman is below 68” tall (emp)
B. a woman is above 60.5” tall (emp)
C. a woman is less than 67” tall (Ncdf)
D. a woman is between 64” and 67” tall (Ncdf)
2. The Chapin Social Insight Test evaluates how accurately someone appraises other people. Scores are
approximately normally distributed with mean µ= 25 and standard deviation σ= 5. The range of
possible scores is 0 to 41.
A. What percentage of the population has scores below 20? (emp)
B. Above 38? (Ncdf)
C. How high must you score in order to be in the top quarter of the population? (Invnorm)
3. The Graduate Record Exam (GRE) is widely used to help predict the performance of applicants to
graduate school. The range of possible scores on the each proportion of the test is 200 to 800. A
university finds that the scores of its applicants on the quantitative proportion of the GRE are
approximately normal with mean µ= 544 and standard deviation σ= 103. Find:
A. The relative frequency of a score greater than 700 (Ncdf)
B. The relative frequency of a score between 500 and 800 (Ncdf)
C. How high you must score to be in the top 10% of the population (Invnorm)
4. The median of any normal distribution is the same as its mean. We can use the standard normal table
to find the quartiles and related descriptive measures for normal distributions.
A. What are the first and third quartiles of the standard normal distribution?
B. What is the value of the IQR for the standard normal distribution?
C. What percent of the observations in the standard normal distribution are suspected outliers
according to the 1.5 x IQR criterions?
Anwers:
1) .84 b) .975 c) Ncdf(-E99, .6)= .726 d) Ncdf(-.6, .6)= .4515 2) .16 b) Ncdf(2.6, E99)= .0046
c) 28.375 3) Ncdf(1.51, E99)= .06 b) .6588 c) over 675.99 4) -.67, .67 b) 1.34 c) .0073