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Statistics / The Practice of Statistics 5 / Chapter 7.3 / Problem 53

The Practice of Statistics | 5th Edition | ISBN: 9781464108730 | Authors: Daren S. Starnes, Josh Tabor

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Larger sample Suppose that the blood cholesterol level of all men aged 20 to 34 follows

Chapter 7, Problem 53

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QUESTION:

Larger sample Suppose that the blood cholesterol level of all men aged 20 to 34 follows the Normal distribution with mean m = 188 milligrams per deciliter (mg/dl) and standard deviation s = 41 mg/dl. (a) Choose an SRS of 100 men from this population. Describe the sampling distribution of x . (b) Find the probability that x estimates m within 3 mg/dl. (This is the probability that x takes a value between 185 and 191 mg/dl.) Show your work. (c) Choose an SRS of 1000 men from this population. Now what is the probability that x falls within 3 mg/dl of m? Show your work. In what sense is the larger sample better?

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QUESTION:

Larger sample Suppose that the blood cholesterol level of all men aged 20 to 34 follows the Normal distribution with mean m = 188 milligrams per deciliter (mg/dl) and standard deviation s = 41 mg/dl. (a) Choose an SRS of 100 men from this population. Describe the sampling distribution of x . (b) Find the probability that x estimates m within 3 mg/dl. (This is the probability that x takes a value between 185 and 191 mg/dl.) Show your work. (c) Choose an SRS of 1000 men from this population. Now what is the probability that x falls within 3 mg/dl of m? Show your work. In what sense is the larger sample better?

ANSWER:

Step 1 of 4

Define a random variable for blood cholesterol level in men aged 20 to 34.

Then,

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