Find three real-life examples of a continuous variable. Which do you may be norm

Question

Find three real-life examples of a continuous variable. Which do you may be normally distributed? Why? In a normal distribution, which is greater, the mean or the median? Explain. What is the total area under the normal curve? What do the inflection points on a normal distribution represent? Where Jo they occur? Draw ,two normal curves that have the same mean but different standard deviations. Describe the similarities and differences. Draw two normal curves that have different means but the same standard deviation. Describe the similarities and differences. What is the mean of the standard normal distribution? What is the standard deviation of the standard normal distribution? Describe how you can transform a nonstandard normal distribution to the standard normal distribution.

Explanation / Answer

2) For a normal distribution : Mean = Median = Mode

3) Total area under a standard normal curve = 1 unit

5) Two normal curve with same mean but different standard deviations would resemble in shape. However, the curve with a bigger standard deviation would have a wider range as opposed to the one with smaller standard deviation.

6) On the other hand when the means are different, but same standard deviations would look like the curve has been displaced a bit to one side.

See the link : https://drherbie.wordpress.com/2006/10/15/normal-distribution-part-ii/

for images and explanations

7) For a standard normal distribution, the mean is 0 and the standard deviation is 1

8) A standard normal distribution can be obtained by applying the following transformation

X ---------> [(X - mean) / S.D ] where mean is the mean of the distribution and S.D is the standard deviation of the distribution

10) [(X - mean) / S.D ] is denoted by Z

Z = 0 would imply that X = mean i.e option C

Hope this helps.

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