nonstandard normal distribution

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The distribution of certain test scores is a nonstandard normal distribution with a mean of 60 and a standard deviation of 4. What are the values of the mean and standard deviation after all test scores have been standardized by converting them to z scores using z = (x - μ)/σ?     

Oct 18th, 2017

Thank you for the opportunity to help you with your question!

After converting them to z , the mean score of z is 0

The standard deviation of z is 1.

This is because E(z) = E((x-mu)/sigma)= (E(x)-mu)/sigma = (60-60)/4=0

sigma( z ) = sigma ( (x-mu)/sigma)= sigma (x-mu) /sigma = 4/4 =1

Answer: mean of z =0

Standard deviation of z = 1 

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Jul 3rd, 2015

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Jul 3rd, 2015

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Jul 3rd, 2015

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