1. Recall on whiteboards What type of data is the normal distribution used to model? Discrete or continuous? About what percentage of the data values will lie within 1 standard deviation of the mean? What are the two parameters of the normal distribution? X ~ N( ?, ? ) Draw on your board the shape you think a normal distribution follows. About what percentage of the data values will lie within 2 standard deviation of the mean? For the STANDARD normal distribution what are the values of

2. Recall on whiteboards On your calculator what are the two letters that help you find probabilities for the normal distribution and write down the how you get to these letters on your calculator? Find P( z < 1.1) Find P(-0.2 < z < 1) Find P( z > -0.75) What is P( z = 2) So what is P( z ≠ 2)

3. Aims: To be able to standardise a Normal distribution. To be able to calculate probabilities of any normal distribution. (By standardising and then using tables or calculator) Continuous Data Lesson 2

4. All normal curves are symmetrical and bell-shaped but the exact shape is governed by 2 parameters – the mean, μ, and the standard deviation, σ. Standardising

5. Which test have I done best in? TEST 1My Score 71 Mean 65 Sd 3 Test 2My Score 79 Mean 70 Sd 5 We will revisit this question at the end and see! Vote!

6. It would of course be impractical to publish tables of probabilities for every possible normal distribution. Fortunately, it is possible and easy to transform any normal distribution to a standard normal: If X ~ then More general normal distributions Example: If, find a) P( X < 23), a)If σ 2 = 16, then σ = 4.

7. b) More general normal distributions Continued: b) P( X > 14);

8. c) More general normal distributions Continued: c) P(16 < X < 24.8).

9. On w/b a) P( X < 10.8); If, find b) P( X > 12.5); c) P(9.9< X < 11.8).

10. More general normal distributions Examination style question: IQs are normally distributed with mean 100 and standard deviation 15. What proportion of the population have an IQ of at least 124? And if a sample of 500 people where chosen at random, how many would you expect to have an IQ of 124 or better? Let X be the r.v ‘the IQ score’ So that X ~ N( )

11. Which test have I done best in? TEST 1My Score 71 Mean 65 Sd 3 Test 2My Score 79 Mean 70 Sd 5 Do Exercise 4C page 105.

12. Last 5 mins – Exam Qu – Can you do it?