Essentials of Statistics (5th Edition)

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

Chapter 5 - Discrete Probability Distributions - 5-3 Binomial Probability Distributions - Page 220: 30

Answer

a)0.0043 b)0.00036 c)0.00479 d)Yes, it is unusually low.

Work Step by Step

a) $P(X=2)={7\choose 2} \cdot (0.2)^5\cdot (0.8)^2=0.0043.$ b)$P(X=1)={7\choose 1} \cdot (0.2)^6\cdot (0.8)^1=0.00036.$ c)$P(X<3)=P(X=0)+P(X=1)+P(X=1)={7\choose 0} \cdot (0.2)^7\cdot (0.8)^0+{7\choose 1} \cdot (0.2)^6\cdot (0.8)^1+{7\choose 2} \cdot (0.2)^5\cdot (0.8)^2=0.00013+0.00036+0.0043=0.00479$ d) Yes, it is an unusually low probability, because 0.00479 is really low, lower than 0.05.
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