Estimating Probabilities Using The Empirical Rule Quiz

1) According to the Empirical Rule, approximately what percentage of data falls within one standard deviation of the mean in a normal distribution?

50%

68%

95%

99.7%

About 68% of data lies within one standard deviation.

Explanation

About 68% of data lies within one standard deviation.

2) In a normal distribution, approximately what percentage of data falls within two standard deviations of the mean?

68%

84%

95%

99.7%

About 95% of data lies within two standard deviations.

Explanation

About 95% of data lies within two standard deviations.

3) The Empirical Rule states that approximately 99.7% of data in a normal distribution falls within how many standard deviations of the mean?

One

Two

Three

Four

99.7% of data lies within three standard deviations.

Explanation

99.7% of data lies within three standard deviations.

4) A set of test scores is normally distributed with a mean of 75 and a standard deviation of 5. Approximately what percentage of students scored between 70 and 80?

34%

50%

68%

95%

70–80 is within one standard deviation (68%).

Explanation

70–80 is within one standard deviation (68%).

5) The heights of adult women in a city are normally distributed with a mean of 65 inches and a standard deviation of 3 inches. Approximately what percentage of women have heights between 59 and 71 inches?

68%

95%

99.7%

100%

59–71 is two standard deviations (95%).

Explanation

59–71 is two standard deviations (95%).

6) A factory produces bolts with lengths that are normally distributed with a mean of 10 cm and a standard deviation of 0.2 cm. Approximately what percentage of bolts have lengths between 9.6 cm and 10.4 cm?

68%

95%

99.7%

50%

9.6–10.4 is two standard deviations (95%).

Explanation

9.6–10.4 is two standard deviations (95%).

7) In a normal distribution, approximately what percentage of data falls above the mean?

34%

50%

68%

95%

The normal curve is symmetric, so half (50%) is above the mean.

Explanation

The normal curve is symmetric, so half (50%) is above the mean.

8) The weights of newborn babies are normally distributed with a mean of 7.5 pounds and a standard deviation of 1 pound. Approximately what percentage of babies weigh between 6.5 and 8.5 pounds?

34%

50%

68%

95%

6.5–8.5 is one standard deviation (68%).

Explanation

6.5–8.5 is one standard deviation (68%).

9) Using the Empirical Rule, if a data set is normally distributed, approximately what percentage of data falls more than three standard deviations away from the mean?

0.3%

2.5%

5%

32%

Only 0.3% of data lies beyond three standard deviations.

Explanation

Only 0.3% of data lies beyond three standard deviations.

10) The daily temperatures in a city during summer are normally distributed with a mean of 80°F and a standard deviation of 5°F. Approximately what percentage of days have temperatures between 75°F and 85°F?

34%

50%

68%

95%

75–85 is within one standard deviation (68%).

Explanation

75–85 is within one standard deviation (68%).

11) Approximately what percentage of students scored between 480 and 560?

34%

50%

68%

95%

480–560 is one standard deviation from the mean (68%).

Explanation

480–560 is one standard deviation from the mean (68%).

12) Approximately what percentage of students scored between 440 and 600?

68%

95%

99.7%

84%

440–600 is two standard deviations (95%).

Explanation

440–600 is two standard deviations (95%).

13) Approximately what percentage of students scored above 560?

16%

32%

50%

84%

Above one standard deviation from the mean is about 16%.

Explanation

Above one standard deviation from the mean is about 16%.

14) Approximately what percentage of students scored below 480?

2.5%

16%

32%

50%

Below one standard deviation is about 16%.

Explanation

Below one standard deviation is about 16%.

15) If there are 800 students in the school, approximately how many students scored between 520 and 560?

136

272

544

680

34% (half of 68%) × 800 = 272 students.

Explanation

34% (half of 68%) × 800 = 272 students.

16) A company measures the time it takes employees to complete a task. The times are normally distributed with a mean of 30 minutes and a standard deviation of 4 minutes. Approximately what percentage of employees complete the task in less than 22 minutes?

0.15%

2.5%

16%

32%

22 is two standard deviations below the mean (2.5%).

Explanation

22 is two standard deviations below the mean (2.5%).

17) The IQ scores in a population are normally distributed with a mean of 100 and a standard deviation of 15. Approximately what percentage of people have IQ scores between 85 and 115?

34%

50%

68%

95%

Within one standard deviation = 68%.

Explanation

Within one standard deviation = 68%.

18) A bakery produces loaves of bread with weights that are normally distributed with a mean of 500 grams and a standard deviation of 10 grams. Approximately what percentage of loaves weigh more than 520 grams?

0.15%

2.5%

16%

50%

520 is two standard deviations above the mean (2.5%).

Explanation

520 is two standard deviations above the mean (2.5%).

19) The amount of rainfall in a region during spring months is normally distributed with a mean of 12 inches and a standard deviation of 2 inches. If the Empirical Rule applies, approximately what percentage of spring months have rainfall between 8 and 16 inches?

68%

95%

99.7%

100%

8–16 is two standard deviations (95%).

Explanation

8–16 is two standard deviations (95%).

20) A teacher finds that quiz scores in her class are normally distributed with a mean of 85 and a standard deviation of 6. She wants to identify students who scored in the top 2.5% of the class. What is the minimum score needed to be in this group?

91

97

103

109

Top 2.5% ≈ two standard deviations above mean → 85 + (2 × 6) = 97.

Explanation

Top 2.5% ≈ two standard deviations above mean → 85 + (2 × 6) = 97.