Essentials of Statistics (5th Edition)

Published by Pearson
ISBN 10: 0-32192-459-2
ISBN 13: 978-0-32192-459-9

Chapter 6 - Normal Probability Distributions - 6-2 The Standard Normal Distribution - Page 252: 50


a)mean=2.5, standard deviation=1.44. b) yes.

Work Step by Step

a) By using the given formula and data:$mean=\frac{max+min}{2}=\frac{5+0}{2}=2.5.$ range=maximum-minimum=5-0=5. standard deviation=$\frac{range}{\sqrt {12}}=\frac{5}{\sqrt {12}}=1.44.$ b)If the standard deviation is 1, then by the given formula we know that the range is $\sqrt {12}$ Then the probability is the range of the given interval divided by the range of the distribution:P(x is between -1 and 1):$\frac{1-(-1)}{\sqrt {12}}=0.5774$ Using the table, the probability of z being between -1 and 1 is equal to the probability of z being less than 1 minus the probability of z being less than -1, which is: 0.8413-0.1587=0.6826 The difference between the results is more than 0.1, which is quite big, hence the answer is yes.
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