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Exercises Probability and the bell curve

Example 5.4 from Statistics, 5.2 The Uniform Distribution

(part 1)

a. What is the probability that a person waits fewer than 12.5 minutes?

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 = the number of minutes a person must wait for a bus. a = 0 and b = 15. X ~ U(0, 15). Write the probability density function. f (x) = $\frac{1}{15 - 0}$ = $\frac{1}{15}$ for 0 ≤ x ≤ 15.
Find P (x < 12.5). Draw a graph.

$P (x < k) = (base) (height) = (12.5 - 0) (\frac{1}{15}) = 0.8333$
The probability a person waits fewer than 12.5 minutes is 0.8333.

Figure 5.15

How did it go?

Previous (part 3)Next (part 2)

From Statistics (High school edition) by OpenStax (Rice University), section 5.2, 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.