Elementary Statistics: Picturing the World (6th Edition)

Published by Pearson
ISBN 10: 0-32191-121-0
ISBN 13: 978-0-32191-121-6

Chapter 5 - Normal Probability Distributions - Section 5.4 Sampling Distributions and the Central Limit Theorem - Exercises - Page 271: 27

Answer

0.15% of sample will have mean salary less than 60000

Work Step by Step

To calculate P(x̄ < 60000), we need to find the z-score: $z = \frac{x̄ - μ_{x̄}}{σ/\sqrt n}$ $= \frac{60000 - 66000}{12000/\sqrt 35}$ = -2.96 P(z < -2.96) = 0.0015, hence: P(x̄ 60000) = 0.0015
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