Chapter 7 Assignment SOLUTIONS WOMEN: Plus, add your pulse rate to the histogram.

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1 Instructor: Linda C. Stephenson WOMEN: Plus, add your pulse rate to the histogram.

2 Instructor: Linda C. Stephenson MEN: Plus, add your pulse rate to the histogram.

1a. For z = -1.17: P (below) = 0.1210 1b. For z = 0.

3859 1c. For z = 0.44: P(below) = 0.3300 For z = 0.

3 1a. For z = -1.17: P (below) = b. For z = 0.29: P(below) = P(above) = = c. For z = 0.44: P(below) = For z = 0.58: P(below) = P(between) = =

1d. For z = 0.86: P(below) = 0.1949 For z = 1.72: P(below) = 0.

225: z = 0.76 (closest area in table is 0.

4 1d. For z = 0.86: P(below) = For z = 1.72: P(below) = P(above) = = P(total) = = For area below = 0.28: z = (closest area in table is ) 3. For area below = 0.225: z = 0.76 (closest area in table is ) Using symmetry, the positive z is: z = = 0.45, divide that equally between the two tails, therefore on each side.

4. Does the STATDISK histogram indicate that a normal distribution could be used as a model for the variable? Yes (yes or no) List the mean : Men: 69.5817, Women: 74.

5 4. Does the STATDISK histogram indicate that a normal distribution could be used as a model for the variable? Yes (yes or no) List the mean : Men: , Women: (bpm) List the standard deviation : Men: , Women: (bpm) List your pulse rate: (bpm) 4a. Minimum usual value = Men: 46.92, Women: (bpm) Maximum usual value = Men: 92.24, Women: (bpm) 4b. Men: Based on the result in part a, would a man with a pulse rate of 95 bpm be considered unusual? Explain why or why not. Women: Based on the result in part a, would a woman with a pulse rate of 95 bpm be considered unusual? Explain why or why not. Men: Yes, it would be unusual, because 95 is greater than the max usual. Women: No, it would NOT be unusual, because 95 is less than the max usual. 4c. z = P(below) = P(above) = =

z = 90 74.04082 1.27 12.54356 P(below) = 0.

5817 0.40 11.3315 P(below) = 0.3446 z95 = 95 69.

6 z = P(below) = P(above) = = d. z65 = P(below) = z95 = P(below) = P(between) = =

z65 = 65 74.04082 0.72 12.54356 P(below) = 0.

54356 P(below) = 0.9525 P(between) = 0.9525 0.

30: z = -0.52 (closest area in table = 0.

68932 bpm For area below = 0.3015) = 74.

7 z65 = P(below) = z95 = P(below) = P(between) = = e. For area below = 0.30: z = (closest area in table = ) = (-0.52)( ) = bpm For area below = 0.30: z = (closest area in table = ) = (-0.52)( ) = bpm

4f. For area below = 0.15: z = 1.04 (closest area in table = 0.1492) 1 0.70 = 0.30, divide that equally between the two tails, therefore 0.15 on each side. = 69.

8 4f. For area below = 0.15: z = 1.04 (closest area in table = ) = 0.30, divide that equally between the two tails, therefore 0.15 on each side. = (-1.04)( ) = bpm The symmetric z- score on the top half is 1.04: = (1.04)( ) = bpm The interval is from 57.8 to 81.4 bpm.

For area below = 0.15: z = 1.04 (closest area in table = 0.1492) = 74.04082 + (-1.04)(12.54356) = 60.9955 bpm The symmetric z- score on the top half is 1.04: = 74.

The area below it will correspond to the percentile. Example: my pulse rate was 90. 90 74.04082 z90 = 1. 27 12.54356 P(below) = 0.898, x100 to get to %.

9 For area below = 0.15: z = 1.04 (closest area in table = ) = (-1.04)( ) = bpm The symmetric z- score on the top half is 1.04: = (1.04)( ) = bpm 4g. The interval is from 61.0 to 87.1 bpm. Calculate your z- score, and find the area below it from the table. The area below it will correspond to the percentile. Example: my pulse rate was z90 = P(below) = 0.898, x100 to get to %. Therefore, I m in about the 90 th percentile. See example to left. Guys, you need to use the men s mean and standard deviation. Therefore, my pulse rate was in the 90 th percentile, because the area below was about 90%.

10 4h. Unusual or not? Explain. Because this is a normal distribution, you can use either the Empirical Rule or the probabilities. Using the Empirical Rule, you already calculated the minimum and maximum usual values above. If your pulse is less than the minimum, or greater than the maximum, then it would be considered unusual. Using the probabilities rule, if your percentile is < 5% or > 95%, it would be considered unusual.

Chapter 7 Assignment SOLUTIONS WOMEN:

Chapter 7 Assignment SOLUTIONS WOMEN: SOLUTIONS WOMEN: MEN: 1a. For z -0.79: P (below) 0.2148 1b. For z 1.46: 0.9279 P(above) 1 0.9279 0.0721 1c. For z 1.23: 0.1093 For z 1.65: 0.9505 P(between) 0.9505 0.1093 0.8412 1d. For z 0.71: 0.2389