Statistics Z Score Question 2

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In a population of exam scores, a score of X = 88 corresponds to z = +2.00 and a score of X = 79 corresponds to z = -1.00. Find the mean and standard deviation for the population. (Hint: Sketch the distribution and locate the two scores on your sketch.)

Oct 26th, 2015

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

 2.0  from the tables is 0.99772
-1.00 from the table is (1-0.8413)=0.1587
thus 

P(x<88)= P(Z < 88−mean/ standard deviation ) = P(Z < 2.00) = 0.9772

P(x<88)= P(Z < 79−mean/ standard deviation ) = P(Z < -1.00) = 0.1587

let  x be the mean and  y  be the standard deviation

hence 88-x/y=0.9772 and  79-x/y=0.1587

here we  form simultaneous equation

88-x=0.9772y

79-x=0.1587y

0.9772y+x=88

0.1587y+x=79

here y = 10.99572 hence x=88-(0.9772*10.99572)

x=88-10.745017584
77.254982
mean=77.254982   standard deviation = 10.99572

Please let me know if you need any clarification. I'm always happy to answer your questions.
Oct 26th, 2015

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