Lec 9 Continuous Probability

Lec 9 Continuous Probability

1. The Normal Distribution

   • Probabilities for the Normal Probability Distribution
     • Standardizing Normal Values = , by calculating its Z value:
     • Using the Table of Cumulative Probabilities for a Standardized Value
       • after finding the z score use the talbe in textbook to find the probability
     • Using NORM.DIST
       • NORM.DIST(value, mean, std deviation, True).
         • The time to download a book to an e-reader is normally distributed, with a mean of 7 seconds, and a standard deviation of 2 seconds.  What is the probability that you can download a book in 9 seconds or less? NORM.DIST(9,7,2,True)=.8413. What is the probability that the download will take more than 9 seconds? This will be 1- P (9 or less) so 1 - .8413 = .1587. What is the probability that the download will take more than 1 second?  1 – P(1 or less)  = 1 – NORM.DIST(1,7,2,True)= .9987

2. The Standard Normal Distribution

   • Probabilities for the Standard Normal Distribution
     • Using NORM.S.DIST = requires only the Z value.
       • •Having found Z=1.00, it is possible to find the probability of observing a            from    NORM.S.DIST(1.00, True), which yields .8413.
     • fine the z score
     • use the text book table
       • The time to download a book to an e-reader is normally distributed, with a mean of 7 seconds, and a standard deviation of 2 seconds.  What is the probability that you can download a book in 9 seconds or less? Answer:  First, find the Z value, and then consult the table. Answer:  Find the Z Value:  Z=(9-7)/2 = 1.00  Then consult the table:  the probability is .8413.

3. Finding an X Value, Given a Probability

   • NORM.INV = requires (probability, mean, std dev
     • :  A certain distribution has a normal distribution, with mean = 7 and standard deviation=2.  At what value of X is there .8413 probability of observations being less than X? NORM.INV(.8413,7,2) = 8.9996

4. Finding a Z Value, Given a Probability

   • NORM.S.INV()

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