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Section 5-1

Section 5-1. Normal Probability Distributions Examples. Page 249 Selected Even Problems, Using the TI-83 #22 Find the area to the left of z = 0.08. 2 nd VARS normalcdf (-10000,.08) = . 5319 # 32 Find the area to the right of z = 2.51 2 nd VARS normalcdf (2.51,10000) = . 0060

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Section 5-1

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  1. Section 5-1 Normal Probability DistributionsExamples

  2. Page 249 Selected Even Problems, Using the TI-83 #22 Find the area to the left of z = 0.08. 2nd VARS normalcdf(-10000,.08) = .5319 #32 Find the area to the right of z = 2.51 2nd VARS normalcdf(2.51,10000) = .0060 #36 Find the area between z = -0.51 and z = 0 2nd VARS normalcdf(-0.51,0) = .1950 #40 Find the area to the left of z= -1.96 or to the right of z= 1.96 Remember that we ADD probabilities for OR questions. 2nd VARS normalcdf(-10000,-1.96) = .025 2nd VARS normalcdf(1.96,10,000) = .025 .025 + .025 = .0500

  3. Page 250, # 42 You are performing a study about the height of 20-29 year old men. A previous study found the height to be normally distributed, with a mean of 69.6 inches and a standard deviation of 3.0 inches. You randomly sample 30 men and find their heights (in inches) to be as follows: Draw a frequency histogram to display these data points using sevenclasses.Is it reasonable to assume that the heights are normally distributed? Why? Find the mean and standard deviation of your sample. Compare the mean and standard deviation of your sample with those in the previous study. Discuss the differences.

  4. Page 250, # 42 You are performing a study about the height of 20-29 year old men. A previous study found the height to be normally distributed, with a mean of 69.6 inches and a standard deviation of 3.0 inches. You randomly sample 30 men and find their heights (in inches) to be as follows: Entering the 30 data points into the TI-83, using STAT and Edit, we can calculate the mean, standard deviation, and median. STAT, Calc, 1-Var Stats gives us what we need. The mean is 68.75, the standard deviation is 2.85, and the median is 69.00.

  5. Max Value: 75.7 Min Value: 62.9 Range: 75.7 – 62.9 = 12.8 Class Width: 12.8/7 = 2 Remember to ROUND UP!! First Lower Limit is the Minimum Value!!! 62.9 64.8 First Upper Limit is one unit less than the 2nd Lower Limit (Remember, our units are tenths, not whole numbers). 64.9 66.8 Add Class Width Down 66.9 68.8 Add Class Width Down 68.9 70.8 70.9 72.8 72.9 74.8 74.9 76.8

  6. Subtract one-half unit from lower limits to get lower boundaries. REMEMBER that our units are tenths!! One-half of a tenth is 5 hundredths (.05) 62.9 62.85 64.85 63.85 64.8 Find the mean of the limits (or boundaries) to find the midpoint of each class. 64.9 66.8 64.85 66.85 65.85 66.9 68.8 66.85 68.85 67.85 68.9 70.8 68.85 70.85 69.85 70.9 72.8 70.85 72.85 71.85 72.9 74.8 72.85 74.85 73.85 Add one-half unit to upper limits to get upper boundaries 74.9 76.8 74.85 76.85 75.85

  7. Count how many data points fit in each class and enter that into the Frequency column 62.9 62.85 64.85 63.85 2 64.8 64.9 66.8 64.85 66.85 65.85 5 66.9 68.8 66.85 68.85 67.85 8 68.9 70.8 68.85 70.85 69.85 8 70.9 72.8 70.85 72.85 71.85 5 72.9 74.8 72.85 74.85 73.85 1 74.9 76.8 74.85 76.85 75.85 1

  8. Draw the histogram using the frequencies obtained from the table we just did. Looking at the histogram drawn from the frequency table, it is easy to see that the data is almost perfectly bell-shaped, symmetrical and centered about the mean. 66.85 62.85 64.85 68.85 70.85 72.85 74.85 76.85 The mean, median, and mode are also very closely bunched together. Mean is 68.75, median is 69.00 and the mode is 69.2 For these reasons, it is reasonable to assume that the heights are normally distributed.

  9. The last part of the question was to compare the mean and standard deviation of your sample with those in the previous study. Discuss the differences. Our mean and standard deviation were 68.75 and 2.85. The previous study had a mean of 69.6 and a standard deviation of 3.0. This means that our sample of men was shorter than the previous study, but that they were also more closely bunched together in height.

  10. Your assignments are: Classwork: Due before you leave today: Pages 248-250, #1-8 All, and #9-41 Odd Homework: Due at the beginning of next class Pages 250-252, #43-61 Odd

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