Question 1137215
<font face="times" color="black" size="3">I'll do part (a) and part (c) as they are different problems; while (b) and (d) are similar to (a) and (c), so I'll leave those for you to try out.


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Part (a)


Plug in x = 25, {{{mu = 30}}} and {{{sigma = 5}}}. Compute to find z.


{{{z = (x-mu)/(sigma)}}}


{{{z = (25-30)/(5)}}}


{{{z = (-5)/(5)}}}


{{{z = -1}}}


The z score is z = -1


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Part (c)


Plug in z = -3, {{{mu = 30}}}, {{{sigma = 5}}}


Solve for x


{{{z = (x-mu)/(sigma)}}}


{{{-3 = (x-30)/(5)}}}


{{{5(-3) = 5*(x-30)/(5)}}} Multiply both sides by 5


{{{-15 = x-30}}}


{{{x-30 = -15}}}


{{{x-30+30 = -15+30}}} Add 30 to both sides


{{{x = 15}}}


The raw score is x = 15. 


Note that if you plugged x = 15 into the equation {{{z = (x-mu)/(sigma)}}}, similar to part (a), then you should get z = -3 which helps confirm the answer.</font>