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Areas Under Any Normal Curve. EXAMPLE : A computer company wants to guarantee their latest laptop. The research department testing has shown that.

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Presentation on theme: "Areas Under Any Normal Curve. EXAMPLE : A computer company wants to guarantee their latest laptop. The research department testing has shown that."— Presentation transcript:

1 Areas Under Any Normal Curve

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5 EXAMPLE : A computer company wants to guarantee their latest laptop. The research department testing has shown that the mean life for the laptop is 30 months with a standard deviation of 4 months. The computer life is normally distributed. The computer company plans to refund the consumer the full purchase price if the laptop fails during the guarantee period. How long can the guarantee period be if management does not want to refund the purchase price on more than 7% of the new laptops ?

6 Areas Under Any Normal Curve EXAMPLE : A computer company wants to guarantee their latest laptop. The research department testing has shown that the mean life for the laptop is 30 months with a standard deviation of 4 months. The computer life is normally distributed. The computer company plans to refund the consumer the full purchase price if the laptop fails during the guarantee period. How long can the guarantee period be if management does not want to refund the purchase price on more than 7% of the new laptops ? So we need to find the z – score value that corresponds to an area under the normal curve to the left that equals 7% or 0.0700 7%

7 Areas Under Any Normal Curve EXAMPLE : A computer company wants to guarantee their latest laptop. The research department testing has shown that the mean life for the laptop is 30 months with a standard deviation of 4 months. The computer life is normally distributed. The computer company plans to refund the consumer the full purchase price if the laptop fails during the guarantee period. How long can the guarantee period be if management does not want to refund the purchase price on more than 7% of the new laptops ? So we need to find the z – score value that corresponds to an area under the normal curve to the left that equals 7% or 0.0700 7% Looking at the z – score table, we look to find the 0.0700 value.

8 Areas Under Any Normal Curve EXAMPLE : A computer company wants to guarantee their latest laptop. The research department testing has shown that the mean life for the laptop is 30 months with a standard deviation of 4 months. The computer life is normally distributed. The computer company plans to refund the consumer the full purchase price if the laptop fails during the guarantee period. How long can the guarantee period be if management does not want to refund the purchase price on more than 7% of the new laptops ? So we need to find the z – score value that corresponds to an area under the normal curve to the left that equals 7% or 0.0700 7% Looking at the z – score table, we look to find the 0.0700 value..00- - -.07.08.09 - - - -1.4 0.080 8 - - - 0.070 8 0.069 4 0.068 1

9 Areas Under Any Normal Curve EXAMPLE : A computer company wants to guarantee their latest laptop. The research department testing has shown that the mean life for the laptop is 30 months with a standard deviation of 4 months. The computer life is normally distributed. The computer company plans to refund the consumer the full purchase price if the laptop fails during the guarantee period. How long can the guarantee period be if management does not want to refund the purchase price on more than 7% of the new laptops ? So we need to find the z – score value that corresponds to an area under the normal curve to the left that equals 7% or 0.0700 7% Looking at the z – score table, we look to find the 0.0700 value..00- - -.07.08.09 - - - -1.4 0.080 8 - - - 0.070 8 0.069 4 0.068 1

10 Areas Under Any Normal Curve What if we wanted to find the z – score for an area to the right ?

11 Areas Under Any Normal Curve

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13 .00- - -.07.08.09 1.8 0.964 1 - - - 0.969 3 0.969 9 0.970 6 1.9 0.971 3 - - - 0.975 6 0.976 1 0.976 7

14 Areas Under Any Normal Curve.00- - -.07.08.09 1.8 0.964 1 - - - 0.969 3 0.969 9 0.970 6 1.9 0.971 3 - - - 0.975 6 0.976 1 0.976 7

15 Areas Under Any Normal Curve.00- - -.07.08.09 1.8 0.964 1 - - - 0.969 3 0.969 9 0.970 6 1.9 0.971 3 - - - 0.975 6 0.976 1 0.976 7

16 Areas Under Any Normal Curve What if we wanted to find the z – score for an area in between ?

17 Areas Under Any Normal Curve 90%

18 Areas Under Any Normal Curve 90%

19 Areas Under Any Normal Curve 90%

20 Areas Under Any Normal Curve 90% - - -.04.05 - 1.6- - - 0.050 5 0.050 0 0.049 5

21 Areas Under Any Normal Curve 90% - - -.040.045.05 - 1.6- - - 0.050 5 0.050 0 0.049 5

22 Areas Under Any Normal Curve 90% - - -.040.045.05 - 1.6- - - 0.050 5 0.050 0 0.049 5

23 Areas Under Any Normal Curve 90% - - -.040.045.05 - 1.6- - - 0.050 5 0.050 0 0.049 5

24 Areas Under Any Normal Curve How do we know a data set is normally distributed ?

25 Areas Under Any Normal Curve How do we know a data set is normally distributed ? Here are a few ways to check : 1.Make a histogram of the data - For a normal distribution, the histogram should be roughly bell – shaped

26 Areas Under Any Normal Curve How do we know a data set is normally distributed ? Here are a few ways to check : 1.Make a histogram of the data -For a normal distribution, the histogram should be roughly bell – shaped

27 Areas Under Any Normal Curve How do we know a data set is normally distributed ? Here are a few ways to check : 1.Make a histogram of the data -For a normal distribution, the histogram should be roughly bell – shaped 3. Use the Pearson’s Index -This method uses an equation to check for skewness (distribution not normal)

28 Areas Under Any Normal Curve How do we know a data set is normally distributed ? Here are a few ways to check : 1.Make a histogram of the data -For a normal distribution, the histogram should be roughly bell – shaped 3. Use the Pearson’s Index -This method uses an equation to check for skewness (distribution not normal) -You need to know the mean, and standard deviation, and median of the data.

29 Areas Under Any Normal Curve How do we know a data set is normally distributed ? Here are a few ways to check : 1.Make a histogram of the data -For a normal distribution, the histogram should be roughly bell – shaped

30 Areas Under Any Normal Curve How do we know a data set is normally distributed ? Here are a few ways to check : 1.Make a histogram of the data -For a normal distribution, the histogram should be roughly bell – shaped

31 Areas Under Any Normal Curve

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