Statistics: Informed Decisions Using Data (4th Edition)

Published by Pearson
ISBN 10: 0321757270
ISBN 13: 978-0-32175-727-2

Chapter 6 - Section 6.2 - Assess Your Understanding - Applying the Concepts - Page 346: 50

Answer

No, it is not unusual.

Work Step by Step

n = 400 and p = 18.4% = 0.184 Expected value (mean): $E(X)=μ_X=np=400\times0.184=73.6$ Standard deviation: $σ_X=\sqrt {np(1-p)}=\sqrt {400\times0.184(1-0.184)}=\sqrt {400\times0.184\times0.816}=7.75$ $np(1-p)=400\times0.184\times0.816=60.0576\gt10$. The probability histogram is bell shaped (see blue rectangle on page 343). There is a probability of 95% that the number of successes is between $μ_X-2σ_X=73.6-2\times7.75=58.1$ and $μ_X+2σ_X=73.6+2\times7.75=89.1$. But, 86 is between 58.1 and 89.1. So, it is not unusual.
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