Quiz 2:Statistical Inference(Data Science Specialization):Answers2025

Question 1

What is the variance of the sample mean of n iid observations (population var = σ²)?

❌ σ²
✅ σ² / n
❌ σ / n
❌ 2σ / √n

Explanation: Variance of the mean of n IID draws = Var( (1/n)∑Xᵢ ) = σ² / n.

Question 2

DBP ~ N(μ=80, σ=10). P(DBP < 70)?

❌ 8%
❌ 32%
❌ 22%
✅ 16%

Explanation: z = (70−80)/10 = −1. Φ(−1) ≈ 0.1587 ≈ 16%.

Question 3

Women brain volume ~ N(1100, 75). 95th percentile?

❌ ~1175
❌ ~1247
❌ ~977
✅ ~1223

Explanation: 95th percentile z ≈ 1.645 → 1100 + 1.645·75 ≈ 1223.4 → ≈1223.

Question 4

Sample mean of n=100 women (σ=75). 95th percentile of sample mean?

❌ ~1088 cc
❌ ~1110 cc
✅ ~1112 cc
❌ ~1115 cc

Explanation: SE = 75/√100 = 7.5. 95th percentile = 1100 + 1.645·7.5 ≈ 1112.34 → ≈1112 cc.

Question 5

Flip fair coin 5 times. P(4 or 5 heads)?

❌ 12%
❌ 6%
❌ 3%
✅ 19%

Explanation: P = [C(5,4)+C(5,5)] / 2⁵ = (5+1)/32 = 6/32 = 0.1875 ≈ 18.75% ≈ 19%.

Question 6

RDI mean=15, sd=10 (not normal). For sample mean of n=100, P(14 < x̄ < 16)?

❌ 34%
✅ 68%
❌ 95%
❌ 47.5%

Explanation: By CLT, SE = 10/√100 = 1. Interval ±1 SD → P(|Z|<1) ≈ 0.6827 → ≈68%.

Question 7

Standard uniform mean=0.5, var=1/12. Sample mean of 1000 obs — expected near?

❌ 0.25
❌ 0.10
❌ 0.75
✅ 0.5

Explanation: Sample mean is unbiased; with large n it concentrates near population mean 0.5.

Question 8

Poisson(5 per hour). Observe 3 hours → Poisson(λ=15). P(X ≤ 10)?

✅ 0.12
❌ 0.08
❌ 0.06
❌ 0.03

Explanation: Approx normal: mean=15, sd=√15≈3.873. z ≈ (10.5−15)/3.873 ≈ −1.16 → Φ(−1.16) ≈ 0.12. So ≈0.12.

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