Problem 1 Given an standardized normal distribution (with mean zero and standard

Question

Problem 1 Given an standardized normal distribution (with mean zero and standard deviation of 1), what is the probability that A. Z is less than 1.08? B. Z is greater than-0.21? C. Z is between -1.28 and 1.33 D. Z is less than 1.57 or greater than 1.99 Problem 2 A statistical analysis of 1,000 long-distance telephone calls made from the headquarter of a the Bricks and Clicks computer corporation indicates that the length of these calls is normally distributed, with mean of 240 seconds and standard deviation of 40 seconds. A. What is the probability that a call lasted less than 180 seconds? B. What is the probability that the call lasted between 180 and 300 seconds? C. What is the probability that the call lasted more than 110 seconds? D. Find the upper quartile of the distribution.

Explanation / Answer

Problem 1

a. P(z<1.08)=0.5+P(0<z<1.08)=0.5+0.3599=0.8599

b. P(z>-0.21)=0.5-P(0<z<-0.21)=0.5+0.0832=0.5832

c. P(-1.28<z<1.33)=P(0<z<1.33)-P(0<z<-1.28)=0.4082+0.3997=0.8079

d. P(z<1.57 or z>1.99)=0.9651

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