E(S)= 0
Anyone for SE(S) and P(S=0) ?
Anyone for SE(S) and P(S=0) ?
Anyone for SE(S) and P(S=0)?
To calculate the probability of each score, we can use the binomial probability formula:
P(X=k) = C(n, k) * p^k * (1-p)^(n-k)
Where:
- P(X=k) is the probability of getting exactly k correct answers
- C(n, k) is the number of combinations of n items taken k at a time (in this case, n is the total number of questions, and k is the number of correct answers)
- p is the probability of getting a single question correct (0.5 in this case since there are two equally likely options)
- n is the total number of questions
Let's calculate the expected value (E(S)).
First, let's calculate the probability of getting each possible number of correct answers:
P(X=0) = C(20, 0) * (0.5)^0 * (1-0.5)^20 = 1 * 1 * 0.5^20 ≈ 0.0000009537
P(X=1) = C(20, 1) * (0.5)^1 * (1-0.5)^19 = 20 * 0.5 * 0.5^19 ≈ 0.0000190735
P(X=2) = C(20, 2) * (0.5)^2 * (1-0.5)^18 = 190 * 0.25 * 0.5^18 ≈ 0.000190735
...
Calculating the probability for each possible score, we get:
P(X=0) ≈ 0.0000009537
P(X=1) ≈ 0.0000190735
P(X=2) ≈ 0.000190735
P(X=3) ≈ 0.0011444107
...
P(X=19) ≈ 0.000190735
P(X=20) ≈ 0.0000009537
Now, let's calculate the expected value (E(S)):
E(S) = 0 * P(X=0) + 1 * P(X=1) + 2 * P(X=2) + 3 * P(X=3) + ... + 20 * P(X=20)
E(S) ≈ 0 * 0.0000009537 + 1 * 0.0000190735 + 2 * 0.000190735 + 3 * 0.0011444107 + ... + 20 * 0.0000009537
Calculate the sum of these terms to get the expected value.
Next, to calculate the standard error (SE(S)), we can use the formula:
SE(S) = sqrt[ Σ{ [X − E(S)]^2 * P(X) } ]
Where Σ represents the sum from X=0 to X=20.
Finally, to calculate the probability of the student getting a score of 0 (P(S=0)), we can simply use the P(X=0) value calculated earlier.
P(S=0) ≈ 0.0000009537
By following these steps and performing the calculations, you should be able to determine E(S), SE(S), and P(S=0) for the given scenario.