Question

Fit a normal curve to the following data
x: 2 4 6 8 10
f: 1 4 6 4 1

Answer 1

Answer on Question #68723 – Math – Statistics and Probability

Question

Fit a normal curve to the following data

x: 2 4 6 8 10

f: 1 4 6 4 1

Solution

$$\mu = \frac {\sum x _ {i} f _ {i}}{\sum f _ {i}} = \frac {9 6}{1 6} = 6.$$ $$\sigma = \sqrt {\frac {\sum f _ {i} (x _ {i} - \mu) ^ {2}}{\sum f _ {i} - 1}} = \sqrt {\frac {6 4}{1 5}} \approx 2. 0 7.$$

Probability density function: $f = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{(x - \mu)^2}{2\sigma^2}} = 0.1927e^{-0.1172(x - 6)^2}$ .

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