【文章內(nèi)容簡(jiǎn)介】 l Probabilities 2022會(huì)計(jì)資訊系統(tǒng)計(jì)學(xué) (一 )上課投影片 . 825 z 0 0. 1 ……. 0. 05 0. 060. 0 0. 0000 0. 0040 0. 0199 0. 02390. 1 0. 0398 0. 0438 0. 0596 0. 636. . . . .. . . . .0. 5 0. 1915 …. …. ….. . . . .? Example continued Finding Normal Probabilities .3413 .5 .1915 2022會(huì)計(jì)資訊系統(tǒng)計(jì)學(xué) (一 )上課投影片 . 826 z 0 0. 1 ……. 0. 05 0. 060. 0 0. 0000 0. 0040 0. 0199 0. 02390. 1 0. 0398 0. 0438 0. 0596 0. 636. . . . .. . . . .0. 5 0. 1915 …. …. ….. . . . .? Example continued Finding Normal Probabilities .1915 .1915 .1915 .1915 .3413 .5 P(Z1) = P(Z0)+ P(0Z1) = .1915 + .3413 = .5328 “Just over half the time, 53% or so, a puter will have an assembly time between 45 minutes and 1 hour” 2022會(huì)計(jì)資訊系統(tǒng)計(jì)學(xué) (一 )上課投影片 . 827 Using the Normal Table (Table 3) ? What is P(Z ) ? 0 P(0 Z ) = .4452 P(Z ) = .5 – P(0 Z ) = .5 – .4452 = .0548 z 2022會(huì)計(jì)資訊系統(tǒng)計(jì)學(xué) (一 )上課投影片 . 828 Using the Normal Table (Table 3) ? What is P(Z ) ? 0 P(0 Z ) P(Z ) = P(Z ) = .5 – P(0 Z ) = .0129 z P(Z ) P(Z ) 2022會(huì)計(jì)資訊系統(tǒng)計(jì)學(xué) (一 )上課投影片 . 829 Using the Normal Table (Table 3) ? What is P(Z ) ? 0 P(Z 0) = .5 P(Z ) = .5 + P(0 Z ) = .5 + .4357 = .9357 z P(0 Z ) 2022會(huì)計(jì)資訊系統(tǒng)計(jì)學(xué) (一 )上課投影片 . 830 Using the Normal Table (Table 3) ? What is P( Z ) ? 0 P(0 Z ) P( Z ) = P(0 Z ) – P(0 Z ) =.4713 – .3159 = .1554 z P( Z ) 2022會(huì)計(jì)資訊系統(tǒng)計(jì)學(xué) (一 )上課投影片 . 831 ? Additional Example 1 ? Determine the following probability: P(Z) P(0Z) = P(Z) 0 P(Z) = = Finding Normal Probabilities 2022會(huì)計(jì)資訊系統(tǒng)計(jì)學(xué) (一 )上課投影片 . 832 ? Additional Example 2 – Determine the following probability: P(Z) P(Z0) = ? 0 P(0Z) = .4678 P(0Z) = .4878 P(Z) = + = =.4878 Finding Normal Probabilities 2022會(huì)計(jì)資訊系統(tǒng)計(jì)學(xué) (一 )上課投影片 . 833 ? Additional Example 3 – Determine the following probability: P(.65Z) .65 0 P(0Z) = .4131 P(0Z.65) = .2422 P(.65Z) = .4131 .2422 = .1709 Finding Normal Probabilities 2022會(huì)計(jì)資訊系統(tǒng)計(jì)學(xué) (一 )上課投影片 . 834 10% 0% 2 0 2 (i) P(X 0 ) = P(Z ) = P(Z 2) 0 10 5 =P(Z2) = Z X ? The rate of return (X) on an investment is normally distributed with mean of 10% and standard deviation of (i) 5%, (ii) 10%. ? What is the probability of losing money? .4772 P(0Z2) = .4772 = .0228 Example Some advice: always draw a picture! 2022會(huì)計(jì)資訊系統(tǒng)計(jì)學(xué) (一 )上課投影片 . 835 10% 0% 1 (ii) P(X 0 ) = P(Z ) 0 10 10 = P(Z 1) = P(Z1) = Z X ? The rate of return (X) on an investment is normally distributed with mean of 10% and standard deviation of (i) 5%, (ii) 10%. ? What is the probability of losing money? .3413 P(0Z1) = .3413 = .1587（ .0228） Example 1 Increasing the standard deviation increases the probability of losing money, which is why the standard deviation (or the variance) is a measure of risk. 2022會(huì)計(jì)資訊系統(tǒng)計(jì)學(xué) (一 )上課投影片 . 836 ? Sometimes we need to find the value of Z for a given probability ? We use the notation zA to express a Z value for which P(Z zA) = A Finding Values of Z zA A 2022會(huì)計(jì)資訊系統(tǒng)計(jì)學(xué) (一 )上課投影片 . 837 ? Example amp。 ? Determine z exceeded by 5% of the population ? Determine z such that 5% of the population is below ? Solution is defined as the z value for which the area on its right under the standard normal curve is .05. 0 Finding Values of Z 2022會(huì)計(jì)資訊系統(tǒng)計(jì)學(xué) (一 )上課投影片 . 838 Finding Values of Z ? Other Z values are ? = ? = 2022會(huì)計(jì)資訊系統(tǒng)計(jì)學(xué) (一 )上課投影片 . 839 Using the values of Z ? Because = and = , it follows that we can state P( Z ) = .95 ? Similarly P( Z ) = .90 2022會(huì)計(jì)資訊系統(tǒng)計(jì)學(xué) (一 )上課投影片 . 840 Exponential Distribution（ 指數(shù)分配） ? The exponential distribution can be used to model ? the length of time between telephone calls ? the length of time between arrivals at a service station ? the lifetime of electronic ponents. ? When the number of occurrences of an event follows the Poisson distribution, the time between occurrences follows the exponential distribution. 2022會(huì)計(jì)資訊系統(tǒng)計(jì)學(xué) (一 )上課投影片 . 841 ? A random variable is exponentially distributed if its probability density function is given by Exponential Distribution ?Note that x ≥ 0. Time (for example) is a nonnegative quantity。 the exponential distribution is often used for time related phenomena such as the length of time between phone calls or between parts arriving at an assembly station. Note also that the mean and standard deviation are equal to each other and to the inverse of the parameter of the distribution (lambda) 2x1)X(V and 1E (X )p a r a m e t e r . ond i s t r i b u t i t he is 0 w he r e0x ,e)x(f???? ?????? ?2022會(huì)計(jì)資訊系統(tǒng)計(jì)學(xué) (一 )上課投影片 . 842 Exponential Distribution ? The exponential distri