Normal Distributions Worksheet

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Normal Distributions Worksheet
MA203 Contemporary Mathematics
Complete the questions on the following pages.
(1) Suppose a data set is represented by a normal distribution with a mean of 125 and a standard deviation
of 7.
(a) What data value is 2 standard deviations above the mean?
(b) What data value is 3 standard deviations below the mean?
(c) What data value is 1.5 standard deviations below the mean?
(d) What data value is 2.5 standard deviations above the mean?
1
(e) What data value is
of a standard deviation above the mean?
5
(2) What are the z-scores for the data values in parts (a)-(e) of the previous question?
(a)
(b)
(c)
(d)
(e)
(3) How do the z-scores from problem (2) correspond to the standard deviations given in problem (1)?
What does this tell you about the relationship between z-scores for a normal distribution and standard
deviation?
(4) Suppose a normal distribution has mean 10 and standard deviation 2. Find the z-scores of the mea-
surements 9, 10, 11, 14, and 17.
(5) In a normally distributed data set, find the value of the standard deviation if the following additional
information is given.
(a) The mean is 226.2 and the z-score for a data value of 230 is 0.2.
σ =
(b) The mean is 9.8 and a z-score for the data value of 10.3 is 2.
σ =
(c) The mean is 14.6 and the z-score for a data value of 5 is
0.3.
σ =
(d) The mean is 577 and the z-score for a data value of 533 is
0.5.
σ =
1

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