A government sample survey plans to measure the total cholesterol level of an SRS of men aged 20-34. Suppose that, in fact, the total cholesterol level of all men aged 20-34 follows the Normal distribution with mean μ=182 milligrams per deciliter (mg/dL) and standard deviation σ=37 mg/dL. Use Table A to answer the questions, where necessary.
(a) Choose an SRS of 100 men from this population. What is the sampling distribution of x̄? (Use the units of mg/dL.)
the N(182,3.7) distribution
What is the probability that x̄ takes a value between 180 and 184 mg/dL? This is the probability that x̄ estimates μ within ±2 mg/dL.
0.4108
(b) Choose an SRS of 1000 men from this population. Now what is the probability that x̄ falls within ±2 mg/dL of μ? (Enter your answer rounded to three decimal places.)
probability: 0.881
The larger sample is much more likely to give an accurate estimate of μ.