Elementary Statistics (12th Edition)

Published by Pearson
ISBN 10: 0321836960
ISBN 13: 978-0-32183-696-0

Chapter 6 - Normal Probability Distributions - 6-3 Applications of Normal Distributions - Beyond the Basics - Page 271: 35


a) Mean:75, standard deviation:10. b)No. c)45.2 and 52.8. d)the method in c)

Work Step by Step

a)If we add 35 to each grade, the mean also increases by 35, it becomes 40+35=75, but the standard deviation remains 10. b)No, because the standard deviation stays the same, hence the scores are not curved. c) By using the table, the z-score corresponding to 0.7 and 1-0.1=0.9: z=0.52 and z= 1.28. Hence the corresponding values:$mean+z⋅standard \ deviation=40+0.52⋅10=45.2.$ $mean+z⋅standard \ deviation=40+1.28⋅10=52.8.$ d) Using the method in c) takes the variation into consideration, whilst the other method doesn't.
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