Exam 2 Practice Test — Chapters 7, 8.1, and 9
Time: 45 minutes · Questions: 12 · Tools: StatCrunch throughout (just like the real exam)
Work each problem in StatCrunch first, then check the answer key at the bottom. Aim for about 3–4 minutes per question.
Chapter 7 — Normal Probability Distribution
1. Adult women’s heights are approximately normal with μ = 64.5 inches and σ = 2.5 inches. What proportion of adult women are taller than 68 inches?
StatCrunch: Stat > Calculators > Normal
2. SAT math scores are approximately normal with μ = 520 and σ = 110. What proportion of test-takers score between 450 and 650?
StatCrunch: Stat > Calculators > Normal
3. A machine fills bags with a normal distribution, μ = 50.0 g and σ = 1.2 g. Find the weight that marks the lightest 2% of bags (the 2nd percentile).
StatCrunch: Stat > Calculators > Normal (use the inverse option)
4. Times to complete a warehouse task are normal with μ = 45 minutes and σ = 8 minutes. What is the probability a randomly selected worker finishes in less than 35 minutes?
StatCrunch: Stat > Calculators > Normal
Section 8.1 — Sampling Distributions
5. A population has μ = 100 and σ = 15. For random samples of n = 25, what is P(x̄ > 104)?
StatCrunch: Stat > Calculators > Normal — enter the standard error (σ/√n) as the SD
6. Bottled water fills are normal with μ = 300 mL and σ = 6 mL. A sample of n = 36 bottles is taken. What is the probability the sample mean is less than 298 mL?
StatCrunch: Stat > Calculators > Normal — enter the standard error as the SD
7. Carry-on bag weights average μ = 22 lb with σ = 5.5 lb. For n = 49 randomly selected bags, find P(21 < x̄ < 23).
StatCrunch: Stat > Calculators > Normal — enter the standard error as the SD
Chapter 9 — Confidence Intervals
8. A sample of n = 64 gives x̄ = 210. The population standard deviation is known: σ = 32. Construct a 95% confidence interval for the population mean μ.
StatCrunch: Stat > Z Stats > One Sample > With Summary
9. A sample of n = 12 gives x̄ = 18.4 and s = 3.2. Construct a 90% confidence interval for μ (σ unknown).
StatCrunch: Stat > T Stats > One Sample > With Summary
10. In a survey of 500 voters, 285 support a ballot measure. Construct a 95% confidence interval for the true proportion p of supporters.
StatCrunch: Stat > Proportion Stats > One Sample > With Summary
11. A 95% confidence interval for mean battery life is (14.2, 17.8) hours. Which statement is correct?
– (a) 95% of batteries last between 14.2 and 17.8 hours.
– (b) We are 95% confident the population mean battery life is between 14.2 and 17.8 hours.
– (c) There is a 95% probability the sample mean falls between 14.2 and 17.8 hours.
12. How large a sample is needed to estimate a population proportion within ±0.03 at 99% confidence, with no prior estimate of p?
Answer Key
- 0.0808 — P(X > 68) with z = 1.40
- ≈ 0.619 — area between z = −0.64 and z = 1.18
- ≈ 47.54 g — z = −2.054 for the 2nd percentile
- 0.1056 — P(X < 35) with z = −1.25
- ≈ 0.091 — SE = 3, z = 1.33
- 0.0228 — SE = 1, z = −2.00
- ≈ 0.797 — SE ≈ 0.786, z = ±1.27
- (202.16, 217.84) — E = 1.96(4) = 7.84
- (16.74, 20.06) — t* = 1.796 (df = 11), E ≈ 1.66
- (0.527, 0.613) — p̂ = 0.57, E ≈ 0.043
- (b)
- 1842 — n = 0.25(2.575/0.03)² = 1841.84, round up