If a random variable X ~ N(82.8, 163.2) what is the Z-Value of 105.7? and What is the probability that X<105.7?

"If a random variable X ~ N(82.8, 163.2) what is the Z-Value of 105.7?"

 

z = (x - mu)/sigma   where mu is the mean and sigma is the standard deviation.

 

z = (105.7 - 82.8)/163.2     (I've assumed the standard deviation is 163.2 here, but if this is the variance then you need to take its square root first).

 

z = 0.14

 

"What is the probability that X<105.7?"

 

For this part of the question use the online normal probability calculator at http://stattrek.com/online-calculator/normal.aspx

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