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.

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?

2)

What first name or nickname would you like us to use?

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

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

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?

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?

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?

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

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?

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?

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

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

13) Approximately what percentage of students scored above 560?

14) Approximately what percentage of students scored below 480?

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

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?

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?

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?

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?

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?