1 / 13

The Normal Distribution

The Normal Distribution . Lesson 2 . Starter: Find P ( Z<1.63). To do this we begin with a sketch of the normal distribution. We then mark a line to represent Z=1.63 P(Z<1.63) is the area under the curve to the left of a. We now use the table to look up this probability

zamir
Télécharger la présentation

The Normal Distribution

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. The Normal Distribution Lesson 2

  2. Starter: Find P (Z<1.63) To do this we begin with a sketch of the normal distribution. We then mark a line to represent Z=1.63 P(Z<1.63) is the area under the curve to the left of a. We now use the table to look up this probability P(Z<1.63) = 0.9484 1.63

  3. Remember this from last lesson! Note this result.. P(Z>a) = 1-P(Z<a)

  4. And we found this really useful result P(Z<-a) = 1 - P(Z<a)

  5. Objectives • Finding the value of Z from a given probability.

  6. Points to note • P(Z<a) is less than 0.5 • a <0 • P(Z<a) is greater than 0.5 • a > 0

  7. Points to note • P(Z>a) is greater than 0.5 • a < 0 • P(Z>a) is less than 0.5 • a > 0

  8. Ex 1 Find the value of a such thatP(Z<a)=0.7852

  9. Ex 1 Find the value of a such thatP(Z<a)=0.7852 Use the table P(Z<a) = 0.7852 a = 0.79 a

  10. Ex 2 Find the value of a such thatP(Z>a)=0.01 P(Z>a) = 0.01 P(Z<a) = 0.990 Look up this result is in the main table. It’s not there! Instead look at the table of Percentage Points to see if p=0.01 is listed. P(Z>a) = 0.01 a = 2.3263 a

  11. Ex 3 Find the value of a such thatP(Z>a)=0.0314 P(Z>a) = 0.0314 P(Z<a) = 1 – P(Z>a) = 1-0.0314 = 0.9686 So from the main table a = 1.86 a a

  12. Ex 4 Find the value of a such that P(Z<a) = 0.0197 The table only lists values for z>0 so we need to reflect the problem in the vertical axis… P(Z<z) = 1 – 0.0197 = 0.9803 From the table z = 2.06 Therefore a = -2.06 a p=0.0197 z p=0.9830

  13. Further Learning: • Read through Example 2 on P180 • Do Ex 9B on P181

More Related