MATH 225N Week 5 Assignment: Evaluating Probability Using the Normal Distribution.
1. Ms. Wilson's math test scores are normally distributed with a
... [Show More] 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.
4. Mr. Karly's math test scores are normally distributed with a mean score of 87 (μ) and a standard deviation of 4 (σ). Using the Empirical Rule, about 99.7% of the data values lie between which two values?
75−99
5. In 2014, the CDC estimated that the mean height for adult women in the U.S. was 64 inches with a standard deviation of 4 inches. Suppose X, height in inches of adult women, follows a normal distribution. Which of the following gives the probability that a randomly selected woman has a height of greater than 68 inches?
16%
6. The number of pages per book on a bookshelf is normally distributed with mean 189 pages and standard deviation 20 pages. What is the probability that a randomly selected book has greater than 229 pages? Use the empirical rule
2.5%
7. After collecting the data, Peter finds that the standardized test scores of the students in a school are normally distributed with mean 85 points and standard deviation 3 points. Use the Empirical Rule to find the probability that a randomly selected student's score is greater than 76 points.
99.85%. [Show Less]