MATH 225N Week 5 Assignment: Evaluating
Probability Using the Normal Distribution
1 . Ms. Wilson's math test scores are normally distributed with a mean score of 73 (μ) and a
standard deviation of 5 (σ). Using the Empirical Rule, about 99.7% of the scores lie
between which two values?
The Empirical Rule says that 99.7% of the data lies within three standard deviations of the
mean. The standard deviation is 5. So, the data that lie within three standard deviations of 73
(between −3σ and 3σ) will be the data that lie in the range that is (5)(3)=15 units less
than the mean (73) and more than the mean (73). So, the values 73−15=58 and
73+15=88 are within three standard deviations of the mean. About 99.7% of the x-
values lie between 58 and 88.
2. Mrs. Miller's geometry test scores are normally distributed with a mean score of 70 (μ) and
a standard deviation of 3 (σ). Using the Empirical Rule, about 95% of the scores lie between
which two values?
The Empirical Rule says that 95% of the data lies within two standard deviations of the mean.
The standard deviation is 3. So, the data that lie within two standard deviations of 70
(between −2σ and 2σ) will be the data that lie in the range that is (3)(2)=6 units less
than the mean (70) and more than the mean (70). So, the values 70−6=64 and
70+6=76 are within two standard deviations of the mean. About 95% of the x-values lie
between 64 and 76.
3. Ms. Wilson's statistics test scores are normally distributed with a mean score of 72 (μ) and
a standard deviation of 3 (σ). Using the Empirical Rule, about 68% of the scores lie between
which two values? 69 and 75.
Probability Using the Normal Distribution
1 . Ms. Wilson's math test scores are normally distributed with a mean score of 73 (μ) and a
standard deviation of 5 (σ). Using the Empirical Rule, about 99.7% of the scores lie
between which two values?
The Empirical Rule says that 99.7% of the data lies within three standard deviations of the
mean. The standard deviation is 5. So, the data that lie within three standard deviations of 73
(between −3σ and 3σ) will be the data that lie in the range that is (5)(3)=15 units less
than the mean (73) and more than the mean (73). So, the values 73−15=58 and
73+15=88 are within three standard deviations of the mean. About 99.7% of the x-
values lie between 58 and 88.
2. Mrs. Miller's geometry test scores are normally distributed with a mean score of 70 (μ) and
a standard deviation of 3 (σ). Using the Empirical Rule, about 95% of the scores lie between
which two values?
The Empirical Rule says that 95% of the data lies within two standard deviations of the mean.
The standard deviation is 3. So, the data that lie within two standard deviations of 70
(between −2σ and 2σ) will be the data that lie in the range that is (3)(2)=6 units less
than the mean (70) and more than the mean (70). So, the values 70−6=64 and
70+6=76 are within two standard deviations of the mean. About 95% of the x-values lie
between 64 and 76.
3. Ms. Wilson's statistics test scores are normally distributed with a mean score of 72 (μ) and
a standard deviation of 3 (σ). Using the Empirical Rule, about 68% of the scores lie between
which two values? 69 and 75.
