Assignment
1. The distribution of a sample of 100 test scores is mound-shaped and symmetrical, with a
mean of 50 and a variance of 144.
a) Approximately how many scores are equal to or greater than 74?
b) What score corresponds to the 75th percentile?
c) If the lowest and highest scores in this sample are 14 and 89, respectively, what is the
range of the scores in standard deviation units?
d) Assume that the 100 test scores still have a mean of 50 and a variance of 144, but
now have a strongly negatively skewed distribution. At least how many of the scores
fall between 32 and 68 in this distribution?
2. A sample of 200 people were given a test. The distribution of the test scores was
mound-shaped and symmetrical with a mean of 100. One person, whose test score was
125, was found to be at the 84th percentile.
a) What is the Z score of a person whose test score is 70?
b) Approximately how many people obtained scores greater than 135?
c) Approximately how many people obtained scores between 65 and 85?
d) Suppose the distribution was not mound-shaped but was skewed. At least how many
people would be expected to obtain scores between 65 and 135?
e) If each person's score was multiplied by 3, what would the test score be of a person
who scored 1.2 standard deviation units below the mean?
3. a) The mean IQ of 200 patients in a psychiatric hospital is 91, with a variance of 16, and
the distribution is highly negatively skewed. Between what two IQ scores would we
expect to find at least 160 of the patients falling?
b) If the distribution was mound-shaped and symmetrical, with the same mean and
standard deviation as in part 'a', approximately how many patients would have IQ scores
at or below the 5th percentile or above a score of 97?
4. Charles Darwin recorded the heights, in inches, of a strange (see part b) species of shrubs
that he discovered on a remote island as follows: "I measured 800 plants. The
distribution of their heights is mound-shaped and symmetrical and has a variance of 9.
One plant, whose height was 4 inches, falls at the 33rd percentile of the distribution".
a) Approximately how many of the 800 plants in this sample are between 8.5 and 10.5
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