Answer:
Explanation:
To find the mean of the probability distribution, we can use the formula:
μ = Σ(x*P(x))
where μ is the mean, x is the number of heads, and P(x) is the probability of getting x heads. We can calculate this using Excel by entering the values for x and P(x) in two columns, and then using the formula "=SUMPRODUCT(A2:A26,B2:B26)" in a third column to find the sum of x*P(x), which gives the mean.
Using this method, we get:
μ = Σ(x*P(x)) = 7.5
So, the mean of the probability distribution is 7.5.
To find the standard deviation, we can use the formula:
σ = sqrt[Σ((x - μ)^2 * P(x))]
where σ is the standard deviation, x is the number of heads, μ is the mean, and P(x) is the probability of getting x heads.
Using Excel, we can first calculate (x-μ)^2 by subtracting the mean from each value of x, squaring the result, and then using the formula "=B2-7.5" and "=C2^2" in two additional columns (assuming the values for x are in column A and the probabilities are in column B).
Next, we can calculate the sum of ((x-μ)^2 * P(x)) using the formula "=SUMPRODUCT(D2:D26,C2:C26)" in a third column.
Finally, we can calculate the standard deviation using the formula "=SQRT(E2)" in a fourth column (assuming the sum of ((x-μ)^2 * P(x)) is in column E).
Using this method, we get:
σ = sqrt[Σ((x - μ)^2 * P(x))] = 2.69 (rounded to two decimal places)
So, the standard deviation of the probability distribution is 2.69 (rounded to two decimal places).