If a binomial distribution applies with a sample size of n = 20, find the expected value, n = 20, p = 0.20.

Question

BlackTom AI · Accepted Answer

To begin, recall that for a binomial distribution, the expected value (mean) is given by E[X] = n × p.

Option 1: 4
- Compute E[X] = 20 × 0.20 = 4. This matches the formula perfectly, so this choice is consistent with the binomial mean.

Option 2: 2
- If you got 2, that would imply E[X] = 2, which would require n × p = 2. Given n = 20 and p = 0.20, the product is 4, not 2. So this option miscalculates the mean based on the provided values.

Option 3: 3
- A mean of 3 would mean n × p = 3. With n = 20 and p = 0.20, we have 4, not 3. This reflects a simple arithmetic error or misapplication of the formula.

Option 4: 5
- Achieving a mean of 5 would require n × p = 5. With the given n and p (20 and 0.20), the product is 4, so 5 is inconsistent with the problem data. This would also imply a different p (0.25) or n (25) if we wanted 5, which are not the provided values.

Overall, the only option that aligns with the binomial mean formula using n = 20 and p = 0.20 is 4, since the expected value is np = 20 × 0.20 = 4.

OSC 2030-009 Fall 2025 SUBMIT: Graded Homework Module 4 (Chap 5)

If a binomial distribution applies with a sample size of n = 20, find the expected value, n = 20, p = 0.20.

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