Math 1600 Laboratory Assignment #11 Page 2 Calculating Percentiles for Normal Random Variables Example: The speed...
Math 1600 Laboratory Assignment #11 Page 2 Calculating Percentiles for Normal Random Variables Example: The speed of cars on a certain stretch of freeway is normally distributed with mean 65 mph and standard deviation 5 mph. Find the 98 percentile of the speeds. Solution Let X - 98 percentile of speeds. Then X = - +Z0-65+Z(5), where is the 98 percentile for Z. We find Z by looking for the probability 9800 in Table 3. It is not there, so we take the two closest probabilities, .9798 and 9803, and interpolate as follows: z P(Z<z) 2.05 .9798 .9800 - 9798 2.06-2.05 .9800 = .0002 .9803 - 9798 -0.01 9800 (98-) 2.06 .9803 = .0005 Z 2054 Z 75,270 X 0.0002 Z=2.05+ 0.01 = 2.05 + (0.4)(0.01) - 2.05 +0.004 - 2.054 0.0005 65 Therefore, X = 1 + Zo - 65+ (2.054)(5) = 65 +10.270 = 75.270. For each part, use Table 3 to find the desired percentile. Shade the appropriate region under the standard normal curve and label the shaded region with the probability, find the corresponding z- value and mark it on the number line on the Z-scale, and then convert the z-value to an X-value and mark it on the number line on the X-scale. Problem: The IQ's in a certain population are normally distributed with mean 104 and standard deviation 14. (a) Find the 67th percentile of IQ's in this population. Z O 104 (b) Find the 20th percentile of IQ's in this population. Z 0 104