Elementary Statistics: A Step-by-Step Approach with Formula Card 9th Edition

Published by McGraw-Hill Education
ISBN 10: 0078136334
ISBN 13: 978-0-07813-633-7

Chapter 6 - The Normal Distribution - Chapter Quiz - Page 365: 24

Answer

a. $0.0038$ b. $0.0228$ c. $0.5$ d. $0.3217$

Work Step by Step

Given $\mu=48,\sigma=3$, use Table E or a calculator: a. $z1=\frac{36-48}{3}=-4, z2=\frac{40-48}{3}=-2.6667$ $P(36\lt X\lt 40)=P(z2)-P(z1)=0.0038-0=0.0038$ b. $z3=\frac{42-48}{3}=-2, P(X\lt 42)=P(z3)=0.0228$ c. $z4=\frac{48-48}{3}=0, P(X\gt48)=1-P(z4)=1-0.5=0.5$ d. $z5=\frac{43-48}{3}=-1.6667, z6=\frac{47-48}{3}=-0.3333$ $P(43\lt X\lt 47)=P(z6)-P(z5)=0.3695-0.0478=0.3217$
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