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Exercises Probability and the bell curve

Example 6.10 from Statistics, 6.2 Using the Normal Distribution

(part 1)

a. Determine the probability that a random smartphone user in the age range 13 to 55+ is between 23 and 64.7 years old.

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. normalcdf(23,64.7,36.9,13.9) = 0.8186

The z-scores are calculated as
$\begin{array}{l} z = \frac{23 - 36.9}{13.9} = \frac{- 13.9}{13.9} = - 1 \\ z = \frac{64.7 - 36.9}{13.9} = \frac{27.8}{13.9} = 2 \end{array}$

The Z-table shows the area to the left of a z-score with an absolute value of 1 to be 0.1587. It shows the area to the left of a z-score of 2 to be 0.9772. The difference in the two areas is 0.8185.
This is slightly different than the area given by the calculator, due to rounding.

How did it go?

Previous (part 2)Next (part 2)

From Statistics (High school edition) by OpenStax (Rice University), section 6.2, 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.