The heights (in cm) for a random sample of 60 males were measured. The sample mean is 166.55, the standard deviation is 12.57, the sample kurtosis is 0.12, and the sample skewness is −0.23. The following table shows the heights subdivided into non-overlapping intervals. Class Observed Expectedpi Height < 150 10 0.09 150 ≤ Height < 160 6 0.21 160 ≤ Height < 170 18 0.31 170 ≤ Height < 180 17 0.25 Height ≥ 180 9 0.14 The heights are subdivided into five intervals. The degrees of freedom for the goodness-of-fit test for normality is ____. A. 2 B. 3 C. 4 D. 5
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
The heights (in cm) for a random sample of 60 males were measured. The sample mean is 166.55, the standard deviation is 12.57, the sample kurtosis is 0.12, and the sample skewness is −0.23. The following table shows the heights subdivided into non-overlapping intervals.
| Class | Observed | Expectedpi |
| Height < 150 | 10 | 0.09 |
| 150 ≤ Height < 160 | 6 | 0.21 |
| 160 ≤ Height < 170 | 18 | 0.31 |
| 170 ≤ Height < 180 | 17 | 0.25 |
| Height ≥ 180 | 9 | 0.14 |
The heights are subdivided into five intervals. The degrees of freedom for the goodness-of-fit test for normality is ____.
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