Empirical and Chebyshev’s Rule Review
1. The 2011 US Open statistician reported that the mean serve speed of the best women tennis
players was 100 miles per hour (mph) and the standard deviation was 10 mph.
a) Assume that the statistician also gave us the information that the distribution of serve speeds was
mound shaped and symmetric
.
What proportion of serves was between
90
mph and
130
mph?
b) If nothing is known about the shape of the distribution,
give an interval of speeds
that will contain
the speeds of
at least 15/16
serves.
c) Suppose that the statistician indicated that the serve speed distribution was
skewed to the right
.
Which of the following values is most likely the value of the
median
serve speed?
a. 105 mph
b. 95 mph
c. 100 mph
d. 108 mph
2. Suppose the average height and standard deviation of 50 students in a class are 66 inch and 3 inch
respectively.
a) If nothing is known
about the shape of the distribution, what proportion represents the number of
students
outside
the
interval
from 60 to 72 inch?
b)
If the heights have a
mound shaped and symmetric
histogram, what proportion of the
observations will be
less than 57
inch?
c)
If the heights have a
mound shaped
and symmetric
histogram, what proportion of the
observations will be
less than 60 and more
than 69 inch?
3
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 Fall '08
 STAFF
 Standard Deviation, Latin honors

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