Answer:
Explanation:
You want the mean and standard deviation of a binomial distribution with n = 6 and p = 1/2.
Mean
You can tell from your table that the distribution is symmetrical about x = 3. That value is the mean.
μ = 3
If you like, you can compute the sum of products of probability and value according to the formula. The first two lines in the attached calculator display show that. The result is μ = 3.
Standard deviation
The attached calculator display shows the sum of products of x² and p(x) is 21/2. Then the standard deviation is ...
σ = √(21/2 -3²)
σ = √(3/2) ≈ 1.22
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Additional comment
It is appropriate to use the exact values of p(x), rather than the rounded values shown in the table.
A calculator or spreadsheet with list-processing capability is useful for this.
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