SOLUTION: A normal distribution has μ = 30 and σ = 5. (a) Find the z score corresponding to x = 25. (b) Find the z score corresponding to x = 44. (c) Find the raw

Algebra ->  Probability-and-statistics -> SOLUTION: A normal distribution has μ = 30 and σ = 5. (a) Find the z score corresponding to x = 25. (b) Find the z score corresponding to x = 44. (c) Find the raw      Log On


   

Question 1137215: A normal distribution has μ = 30 and σ = 5.
(a) Find the z score corresponding to
x = 25.


(b) Find the z score corresponding to
x = 44.



(c) Find the raw score corresponding to
z = −3.



(d) Find the raw score corresponding to
z = 1.7.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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+=+%28x-mu%29%2F%28sigma%29

z+=+%2825-30%29%2F%285%29

z+=+%28-5%29%2F%285%29

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+=+%28x-mu%29%2F%28sigma%29

-3+=+%28x-30%29%2F%285%29

5%28-3%29+=+5%2A%28x-30%29%2F%285%29 Multiply both sides by 5

-15+=+x-30

x-30+=+-15

x-30%2B30+=+-15%2B30 Add 30 to both sides

x+=+15

The raw score is x = 15.

Note that if you plugged x = 15 into the equation z+=+%28x-mu%29%2F%28sigma%29, similar to part (a), then you should get z = -3 which helps confirm the answer.