Answer:
Upper P60 = 212.8
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean
and standard deviation
, the zscore of a measure X is given by:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
![\mu = 200, \sigma = 50](https://tex.z-dn.net/?f=%5Cmu%20%3D%20200%2C%20%5Csigma%20%3D%2050)
Find Upper P 60, the score which separates the lower 60% from the top 40%.
This is the value of X when Z has a pvalue of 0.6. So it is X when Z = 0.255.
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![0.255 = \frac{X - 200}{50}](https://tex.z-dn.net/?f=0.255%20%3D%20%5Cfrac%7BX%20-%20200%7D%7B50%7D)
![X - 200 = 0.255*50](https://tex.z-dn.net/?f=X%20-%20200%20%3D%200.255%2A50)
![X = 212.8](https://tex.z-dn.net/?f=X%20%3D%20212.8)
Upper P60 = 212.8