A population of values has a normal distribution with mean of 159.4 and standard deviation of 80.5.  a) Get the z-score for a value of 144.1. For this problem you use the z score formula z=x−μσz=x-μσ    b) This z-score tells you how many  the score of 144.1 is above or below the population mean μμ . c) Find the probability that a randomly selected value is greater than 144.1.

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A population of values has a normal distribution with mean of 159.4 and standard deviation of 80.5. 

a) Get the z-score for a value of 144.1. For this problem you use the z score formula z=x−μσz=x-μσ   

b) This z-score tells you how many  the score of 144.1 is above or below the population mean μμ .

c) Find the probability that a randomly selected value is greater than 144.1.  

Expert Solution
Step 1

a)

A population value has a normally distributed with mean 159.4 and standard deviation 80.5.

The z score is calculated as follows:

Z= (144.1-159.4)/80.5

  = -0.1901

Thus, the z score is -0.1901

b)

The z-score tells that the score of 144.1 is 0.1901 standard deviation below the population mean μ.

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