This preview shows page 1. Sign up to view the full content.
Unformatted text preview: We have converted our normal distribution for height into the Z distribution. On the Z-axis (Z-scale): The mean of 65 is now 0. The standard deviation of 1.5 is now 1. The X of 67 is now 1.33. We can use this data to answer the question in this problem. The table tells shows 0.9082, which means 90.82% of the area under the curve is to the left of Z=1.33. That means, approximately 91% of the females are shorter than 67 inches. Automatically, we can also conclude that approximately 9% of the area under the curve is to the right of Z=1.33. Therefore, the probability that a woman is taller than 67 inches is approximately 0.09. Also, since the curve is symmetrical, 50% of it is to the right of the mean and 50% of it is to the left of the mean. Therefore, since approximately 9% is above 67 inches, then approximately 41% (50% - 9%) is between 65 and 67 inches (i.e., 41% is between Z values of 0 and 1.33)....
View Full Document
- Spring '08