Final answer:
a. The value above which 2.5% of the data lies is 88.6. b. The value below which 16% of the data lies is 104.09. c. 50% of the data is above 135. d. 2.28% of the data is below 90.
Step-by-step explanation:
a. To find the value above which 2.5% of the data lies, we need to find the z-score corresponding to this percentile. We can use the z-table or a calculator to find that the z-score for 2.5% is approximately -1.96. Now, we can use the formula z = (x - mean) / standard deviation to find the value x. Rearranging the formula, we get x = mean + (z * standard deviation). Plugging in the values, we get x = 120 + (-1.96 * 15) = 88.6.
b. To find the value below which 16% of the data lies, we can use a similar approach. The z-score for 16% is approximately -0.994. Using the formula, we get x = 120 + (-0.994 * 15) = 104.09.
c. To find the percent of the data that is above 135, we need to find the z-score for this value. The z-score is given by z = (x - mean) / standard deviation. Rearranging the formula, we get x = mean + (z * standard deviation). Plugging in the values, we get x = 120 + ((135 - 120) / 15) = 125. The percent of the data above 135 is 100% - the percent below 135, so it is 100% - 50% = 50%.
d. To find the percent of the data below 90, we can use the same approach as in part c. The z-score for 90 is given by z = (90 - 120) / 15 = -2. The percent of data below 90 is the same as the percent below the z-score -2, which is approximately 2.28%. Therefore, the percent of data below 90 is 2.28%.