1 / 13

Normal distribution (2)

Normal distribution (2). When it is not the standard normal distribution. The Normal Distribution. WRITTEN :. … which means the continuous random variable X is normally distributed with mean  and variance  2 (standard deviation  ). The Standard Normal Distribution.

davidclark
Download Presentation

Normal distribution (2)

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Normal distribution (2) When it is not the standard normal distribution

  2. The Normal Distribution WRITTEN : … which means the continuous random variable X is normally distributed with mean  and variance 2 (standard deviation )

  3. The Standard Normal Distribution • The random variable is called Z • Z is called the standard normal distribution • its mean  is 0 • standard deviation  is 1 • The distribution function is denoted by  • Area under the curve = probability (Z)

  4. (-1.6) = P(Z<-1.6) By symmetry: (1.6) =1 - (-1.6) P(Z<-1.6) = 1 - P(Z<1.6) The Standard Normal Distribution The probabilities are given by the area under the curve =0.0548

  5. Probability above 75?

  6. The Normal Distribution The Standard Normal Distribution • Tables are for standardised Z • May want to find other solutions (given  and 2) • The normal distributions must be ‘standardised’ • However, GDCs can handle either

  7. Use the transformation Standardising …. then, use probability table for Z

  8. Probability above 75? P(X>75) = 1 - P(X<75) = 1 - 0.8413 = 0.1587 1 - P(Z<1) 1 - P(X<75)

  9. Probability between 65 and 70? = P(X<70) - P(X<65) P(65<X<70)

  10. Probability between 65 and 70? = P(X<70) - P(X<65) P(65<X<70) P(-1<Z<0) - P(Z<-1) P(Z<0) - [1- P(Z<1)] P(Z<0) - [1 - 0.8413] = 0.3413 0.5

  11. Probability between 65 and 70? Why not GDC? normalcdf(lower bound, upper bound, mean (), standard deviation ()) P(65<X<70) distr 2 normalcdf(65, 70, 70, 5) 2nd P(-1<Z<0) distr 2 normalcdf(-1, 0) 2nd (if you close bracket it assumes ‘Z’)

  12. Very very big Probability above 75? normalcdf(lower bound, upper bound, mean (), standard deviation ()) No upper bound!!!! distr 2 normalcdf(75, E99, 70, 5) 2nd

  13. Very very small Probability below 65? normalcdf(lower bound, upper bound, mean (), standard deviation ()) No lower bound!!!! distr 2 normalcdf(-E99, 65, 70, 5) 2nd

More Related