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 - 6-7 Normal as Approximation to Binomial - Page 307: 20


0.2709, the observed rate could be possible.

Work Step by Step

p=0.00034 $q=1-p=1-0.00034=0.99966$ $n⋅p=420095⋅0.00034=143≥5.$ $n⋅q=420095⋅0.99966=419952≥5.$ Hence, the requirements are satisfied. mean: $\mu=n\cdot p=420095\cdot0.00034=142.8323.$ standard deviation: $\sigma=\sqrt{n\cdot p\cdot q}=\sqrt{420095\cdot0.00034\cdot0.99966}=11.9492.$ 135.5 is the first value more than 135, hence: $z=\frac{value-mean}{standard \ deviation}=\frac{135.5-142.8323}{11.9492}=-0.61.$ By using the table, the probability belonging to z=-0.72: 0.2358, hence the probability: 0.2709. This probability is not too close to 0, therefore the observed rate could be possible.
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