Normal Distributions Worksheet Page 2
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3Normal Distributions Worksheet
MA203 Contemporary Mathematics
(6) Suppose that there are 100 franchises of Betty’s Boutique in similar shopping malls across America.
The gross Saturday sales of these boutiques are approximately normally distributed with $4610 and a
standard deviation of $370.
(a) Find the z-scores of each of the following gross Saturday sales amounts: $3870, $4425, and $5535.
(b) What percentage of Betty’s Boutique franchises had gross Saturday sales between $4425 and $5535?
Use the z-scores you found in part (a) and the z-score table from class.
(c) What percentage had gross Saturday sales between $3870 and $5535? Use the z-scores you found
in part (a) and the z-score table from class.
(d) What percentage of stores had gross Saturday sales less than $5535?
(7) Suppose that a certain insect has a mean lifespan of 5.6 days with a standard deviation of 1.2 days.
Assume that the lifespan of this insect is approximately normally distributed.
(a) Calculate the percentage of insects with a life-span between 3.2 and 8 days.
(b) Calculate the percentage of insects with a life-span between 2.6 and 8.6 days.
(c) What percentage of insects will live longer than 3.32 days?
(d) What percentage of insects will live less than 6.56 days?
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