# Chapter 6 - Normal Probability Distributions - 6-7 Normal as Approximation to Binomial - Basic Skills and Concepts - Page 312: 15

a) $0.0318$ b) $0.2676$ c) Part ) d) No

#### Work Step by Step

a. We find: $μ=np=(580)(0.75)=435$ $σ=\sqrt{npq}=\sqrt{(580)(0.25)(0.75)}=10.43$ Hence, we find z: $z=\frac{428.5−435}{10.43}=−0.62$ $z=\frac{427.5−435}{10.43}=−0.72$ Thus, using the table of z-scores, we can find that the corresponding probability is: $0.0318$. b) We find z: $z=\frac{428.5−435}{10.43}=−0.62$ Thus, using the table of z-scores, we can find that the corresponding probability is $0.2676$. c) Part b) is more useful, because we want to consider the higher value. d) No, there is not. Although $26.76$ percent is low, it is not low enough to prove that the study was wrong.

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