MATH 225N Week 5 Assignment: Evaluating Probability Using the Normal Distribution.

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