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# Nov 4 Normal Distribution

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### Nov 4 Normal Distribution

1. 1. Normal Distribution  Data samples are often collected from very large populations.  the heights of G rade 12 studen ts in Manitoba the number of CDs sold monthly omo biles anc y of new aut th e life expect 1
2. 2. 2
3. 3. 3
4. 4. A histogram of the test results for a larger population of students • smooth curve is bell shaped.  • scores are clustered around the  mean score.  • symmetrical on either side of the  mean.  • very few students scored less than  45 or greater than 85.  4
5. 5. 34% 34% .15% 13.5% 13.5% .15% 2.35% 2.35% Every normal curve has the following characteristics:  • bell shaped and extends in both directions.  • mean is at the centre of the curve and the curve is symmetrical about the mean.  • mean equals the median.  • scores tend to cluster around the middle with very few values more than three standard  deviations away from the mean on either side.  • 68% (34% + 34%) of all the data falls within one standard deviation of the mean.  • 17% (13.5% + 13.5%) of all data falls between one and two standard deviations of the  mean.  • 4.7% (2.35% + 2.35%) of all data falls between two and three standard deviations of the  mean.  5
6. 6. Example 1: Characteristics of a Normal Distribution  6
7. 7. Normal distributions come in different sizes and shapes. Depending on the mean and standard deviation, a normal curve may be flat and spread out or tall and skinny. 7
8. 8. • Find the mean and standard deviation (Sx)  • What percent of data are approximately within      two standard deviations of the mean? 8
9. 9. • st a nd = ar n = dd ea ev m • ia tio n (S x ) 9
10. 10. 34% 34% .15% 13.5% 13.5% .15% 2.35% 2.35% 66 68 70 72 74 76 78 a) State the mean and standard deviation of heights.  b) Find the percent of players that are between 68 in. and 74 in. tall  c)Find the percent of players that are over 74 in. tall.  d) Find the number of players that are over 74 in. tall.  10
11. 11. The personnel manager of a business employing 50 people finds  that the annual average employee salary is \$36,000 with a standard  deviation of \$8000. The data is normally distributed.  34% 34% .15% 13.5% 13.5% .15% 2.35% 2.35% • Find the percentage of employees who earn   more than \$28,000 annually.  • Find the number of employees who earn less  than \$20,000 or more than \$44,000 annually.  11
12. 12. 34% 34% .15% 13.5% 13.5% .15% 2.35% 2.35% 12
13. 13. Assignment 3 Statistics Handbook pg. V‑F‑21 to V‑F‑24 13