Need help.....A set of exam scores are reported as X values and z-scores. On this exam a score of X=75 corresponds to a z-score of z=1.00 and X=60 corresponds to a z-score of z=-0.50. What are the values for the mean and the standard deviation for this exam ?

Question

anonymous · Answer

Use the formula:$$z=\frac{x-\mu}{\sigma}$$You have two equations (one for x=75, and one for x=60).  With two equations and two unknowns you can solve this system by elimination or substitution.

anonymous · Answer

Okay....For the first equation I got $$\sigma =10 and \mu = 65$$ Having difficulties with the second equation

anonymous · Answer

$$\sigma=75-\mu $$ (1) 

and$$-0.5\sigma=60-\mu $$Multiplying the second by -2 gives:
$$\sigma=2\mu-120$$ (2)
Subtracting (1) from (2):
$$0=3\mu-195$$so,$$\mu=195$$The mean is the same for both equations so pick one and use mean=195 and solve for std. dev.

anonymous · Answer

Thank You so very much...I really appreciate your help

anonymous · Answer

ooops, forgot to divide the 195 by 3.  
3*mean=195
mean=65

anonymous · Answer

so yeah, the std. dev is 10 as you said :)

anonymous · Answer

Would 10 be the standard deviation for both