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 5.5 Normal Approximations to Binomial Distributions - Exercises - Page 282: 20

Answer

Answer: Yes, we can use the normal distribution to approximate the binomial. Hence, Mean = 22 and Standard Deviation $\approx $3.146.

Work Step by Step

n = 40, p = 0.55, q = 0.45 np = 40 x 0.55 = 22 nq = 40 x 0.45 = 18 Remember: If np $\geq$ 5 and nq $\geq$ 5, we can use the normal distribution to approximate the binomial. Since np $\geq$ 5 and nq $\geq$ 5, we can use the normal distribution to approximate the binomial. Hence: Mean = np = 22 Standard Deviation = $\sqrt{npq}$ = $\sqrt {40\times 0.55\times0.45}$ $\approx$ 3.146
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