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Exercises Probability and the bell curve

Example 7.1 from Statistics, 7.1 The Central Limit Theorem for Sample Means (Averages)

(part 1)

a. Find the probability that the sample mean is between 85 and 92.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
a. Let X = one value from the original unknown population. The probability question asks you to find a probability for the sample mean.

Let $\bar{X}$ = the mean of a sample of size 25. Because μ_x = 90, σ_x = 15, and n = 25,

$\bar{X} \sim N (μ_{x}, \frac{σ_{x}}{\sqrt{n}})$

Find P(85 < $\bar{x}$ < 92). Draw a graph.

P(85 < $\bar{x}$ < 92) = 0.6997

The probability that the sample mean is between 85 and 92 is 0.6997.

How did it go?

Previous (part 3)Next (part 2)

From Statistics (High school edition) by OpenStax (Rice University), section 7.1, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.