Question

Questions 12-15. Data from Ivy Tech’s advising center shows that their wait times follow a normal distribution. Use theEmpirical Rule to answer the following questions. 5 10 15 20 25 30 3512. What percent of students will wait between 15 and 25 minutes? (round to the nearest whole number)13. What percent of students will wait less than 20 minutes? (round to the nearest whole number)14. What percent of students will wait more than 35 minutes? (round to the hundredths place)15. If 5,300 students come to the advising center, how many students would wait more than 35 minutes? (round to thenearest student)

Answer 1

12. 68%

13. 50%

14. 0.15%

15. 8 students

Explanation:

Given a normal distribution with mean 20 and standard deviation 5, you want several probabilities based on the empirical rule.

Empirical rule

The empirical rule tells you the percentages of a normal distribution that are within 1, 2, or 3 standard deviations of the mean. They are ...

• within 1: 68%
• within 2: 95%
• within 3: 99.7%

12. Between 15 and 25

Wait times between 15 and 25 are within 20±5, so within 1 standard deviation of the mean. The percentage of students waiting 15–25 minutes is 68%.

13. Less than 20

The mean of the distribution is 20, which is its line of symmetry.

50% of students will wait less than 20 minutes.

14. More than 35

35 is 3 standard deviations above the mean, so the fraction in this group is half of the difference between 1 and 99.7%.

0.15% of students will wait more than 35 minutes.

15. How many?

Of 5300, the number waiting more than 35 minutes is ...

0.15% × 5300 = 7.95 ≈ 8

About 8 students will wait more than 35 minutes.

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Additional comment

These values are based on the empirical rule, as required by the problem statement. The actual number for P(Z>3) is about 0.0013499 (0.13%), and the number of students is about 7.15 ≈ 7. That is, the result using the empirical rule is slightly different than what you get using a calculator, spreadsheet, or table.

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