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Calculations of Probabilities

Module by: Susan Dean, Barbara Illowsky, Ph.D.. E-mail the authors

Probabilities are calculated by using technology. There are instructions in the chapter for the TI-83+ and TI-84 calculators.

Note:

In the Table of Contents for Collaborative Statistics, entry 15. Tables has a link to a table of normal probabilities. Use the probability tables if so desired, instead of a calculator. The tables include instructions for how to use then.

Example 1

If the area to the left is 0.0228, then the area to the right is 1 - 0.0228 = 0.9772 1-0.0228=0.9772.

Example 2

The final exam scores in a statistics class were normally distributed with a mean of 63 and a standard deviation of 5.

Problem 1

Find the probability that a randomly selected student scored more than 65 on the exam.

[ Show Solution ]

Problem 2

Find the probability that a randomly selected student scored less than 85.

[ Show Solution ]

Problem 3

Find the 90th percentile (that is, find the score k that has 90 % of the scores below k and 10% of the scores above k).

[ Show Solution ]

Problem 4

Find the 70th percentile (that is, find the score k such that 70% of scores are below k and 30% of the scores are above k).

[ Show Solution ]

Example 3

A computer is used for office work at home, research, communication, personal finances, education, entertainment, social networking and a myriad of other things. Suppose that the average number of hours a household personal computer is used for entertainment is 2 hours per day. Assume the times for entertainment are normally distributed and the standard deviation for the times is half an hour.

Problem 1

Find the probability that a household personal computer is used between 1.8 and 2.75 hours per day.

[ Show Solution ]

Problem 2

Find the maximum number of hours per day that the bottom quartile of households use a personal computer for entertainment.

[ Show Solution ]

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