## Question 385:

1## Answer:

No answer provided yet.Calculate z-scores to answer this question by subtracting the data-point from the mean and divide that result by the standard deviation. From the z-score you can then look-up the proportion of area under the normal curve to answer the questions using the z-score to percentile calculator. Depending on what the question is asking you will either use the 1-sided or 2-sided area.

- <= 12km : (12-10)/3 = a z-score of .666. Since this is asking within 12km we want the area up to .666 or the 1-sided area. Since the z-score is positive we will want the larger area = 74.7% of the area.
- > 15km : (15-10)/3 = 1.666 and we want the smaller area since it is asking for the area NOT under the curve = 4.8%
- The closest 10% have a 1-sided z-score of -1.28. Setting up an equation:
- (x-10)/3 = -1.28
- x-10 = 3*-1.28
- x = 10-3.84
- x = 6.16
- So the closest 10% live within 6.16km.

- Finally, the furthest 33% (or the closest 66%) have a 1-sided z-score of .4124. Setting up an equation:
- (x-10)/3 = .412
- x-10 = 3*.412
- x = 10+1.236
- x = 11.236
- So 33% live further than 11.236 km away.

You can visualize this relationship using the interactive graph of the standard normal curve. Enter the mean of 10 and standard deviation of 3 in the graphs to see the areas.