# ch06 - 6.1 The probability distribution of a discrete...

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6.1 The probability distribution of a discrete random variable assigns probabilities to points while that of a continuous random variable assigns probabilities to intervals. 6.3 Since P ( a ) = 0 and P ( b ) = 0 for a continuous random variable, ( P a a P b x ( ) = ) b x < < . 6.5 The standard normal distribution is a special case of the normal distribution. For the standard normal distribution, the value of the mean is equal to zero and the value of the standard deviation is 1. In other words, the units of the standard normal distribution curve are denoted by z and are called the z values or z scores. The z values on the right side of the mean (which is zero) are positive and those on the left side are negative. The z value for a point on the horizontal axis gives the distance between the mean and that point in terms of the standard deviation. 6.7 As its standard deviation decreases, the width of a normal distribution curve decreases and its height increases. 6.9 For a standard normal distribution, z gives the distance between the mean and the point represented by z in terms of the standard deviation. 6.11 Area between σ μ 5 . 1 - and σ μ 5 . 1 + is the area from 50 . 1 - = z to 50 . 1 = z , which is: ) 5 . 1 5 . 1 ( - z P 8664 . 0668 . 9332 . ) 5 . 1 ( ) 5 . 1 ( = - = - - = z P z P 6.13 Area within 2.5 standard deviations of the mean is: 9876 . 0062 . 9938 . ) 5 . 2 ( ) 5 . 2 ( ) 5 . 2 5 . 2 ( = - = - - = - z P z P z P 6.15 a. 4744 . 5000 . 9744 . ) 0 ( ) 95 . 1 ( ) 95 . 1 0 ( = - = - = < < z P z P z P b. 4678 . 0322 . 5000 . ) 85 . 1 ( ) 0 ( ) 0 85 . 1 ( = - = - - = < < - z P z P z P c. 1162 . 8749 . 9911 . ) 15 . 1 ( ) 37 . 2 ( ) 37 . 2 15 . 1 ( = - = - = < < z P z P z P d. 0610 . 0020 . 0630 . ) 88 . 2 ( ) 53 . 1 ( ) 53 . 1 88 . 2 ( = - = - - - = - - z P z P z P e. 9452 . 0475 . 9927 . ) 67 . 1 ( ) 44 . 2 ( ) 44 . 2 67 . 1 ( = - = - - = - z P z P z P 6.17 a. 0594 . 9406 . 1 ) 56 . 1 ( 1 ) 56 . 1 ( = - = - = z P z P b. 0244 . ) 97 . 1 ( = - z P c. 9798 . ) 05 . 2 ( ) 05 . 2 ( 1 ) 05 . 2 ( = = - - = - z P z P z P d. 9686 . ) 86 . 1 ( ) 86 . 1 ( = - = < z P z P

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6.19 a. 5 . 5 . 1 ) 0 ( ) 28 . 4 ( ) 28 . 4 0 ( = - = < - < = < < z P z P z P approximately b. 5 . 0000 . 5 . ) 75 . 3 ( ) 0 ( ) 0 75 . 3 ( = - = - < - < = - z P z P z P approximately c. 0000 . ) 43 . 7 ( ) 43 . 7 ( = - = z P z P approximately d. 0000 . ) 49 . 4 ( = - < z P approximately 6.21 a. 9613 . 0336 . 9949 . ) 83 . 1 ( ) 57 . 2 ( ) 57 . 2 83 . 1 ( = - = - - = - z P z P z P b. 4783 . 5 . 9783 ) 0 ( ) 57 . 2 ( ) 02 . 2 0 ( = - = - = z P z P z P c. 4767 . 5 . 9767 . ) 0 ( ) 99 . 1 ( ) 0 99 . 1 ( = - = - = - z P z P z P d. 0694 . ) 48 . 1 ( ) 48 . 1 ( = - < = z P z P 6.23 a. 0162 . ) 14 . 2 ( = - < z P b. 2450 . 7486 . 9936 . ) 67 . ( ) 49 . 2 ( ) 49 . 2 67 (. = - = - = z P z P z P c. 1570 . 0192 . 1762 . ) 07 . 2 ( ) 93 . ( ) 93 . 07 . 2 ( = - = - - - = - - z P z P z P d. 9625 . ) 78 . 1 ( = < z P 6.25 a. 8365 . ) 98 . ( ) 98 . ( = < = - z P z P b. 8762 . 0068 . 8830 . ) 47 . 2 ( ) 19 . 1 ( ) 19 . 1 47 . 2 ( = - = - - = - z P z P z P c. 5 . 5000 . 1 ) 0 ( ) 25 . 4 ( ) 25 . 4 0 ( = - = - = z P z P z P approximately d. 5 . 0000 . 5000 . ) 36 . 5 ( ) 0 ( ) 0 36 . 5 ( = - = - - = - z P z P z P approximately e.
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