week 10

Question 1

Card M1

Answer 1

Card M2

Question 2

What is the formula for the Standard Deviation of the Sample Mean?

Answer 2

σₓ̄ = σ / √n

Question 3

State the Central Limit Theorem (CLT) condition for X̄ to be approximately Normal.

Answer 3

Sample size n must be large (commonly n ≥ 30) and samples drawn independently from the population.

Question 4

Define Standard Error (SE) when population σ is unknown.

Answer 4

SE(X̄) = s / √n, where s is the sample standard deviation.

Question 5

What is the formula for the sample proportion’s Standard Error?

Answer 5

SE(p̂) = √[p̂(1 − p̂) / n]

Question 6

What does FPCF (Finite Population Correction Factor) adjust for?

Answer 6

It reduces the standard deviation estimate when sampling without replacement and n ≥ 10% of the population.

Question 7

Write the FPCF formula.

Answer 7

√[(N−n)/(N−1)]

Question 8

When do you apply a t-distribution instead of z-distribution for X̄?

Answer 8

When σ (population st.dev.) is unknown and the sample standard deviation s is used.

Question 9

What is the z-score formula for X̄ when σ is known?

Answer 9

z = (X̄ − μ) / (σ / √n)

Question 10

State the Continuity Correction offset for binomial approximations.

Answer 10

Use ±0.5 on the boundary (e.g., k+0.5) before converting to z-scores in Normal approximation.

Question 11

List one key sampling bias to avoid.

Answer 11

Convenience sampling—it leads to non-representative data and distorts results.

Question 12

What does “10% condition” refer to?

Answer 12

If sampling without replacement, the sample size n should be at most 10% of the population N.

Question 13

Summarize the main steps to find the probability of exceeding a railcar’s max load.

Answer 13

Identify n, μ, σ. Compute μ_Y = nμ. Compute σ_Y = √n * σ. Apply FPCF if needed. Convert to z or t and find area above threshold.