SOLUTION: A normal distribution has 𝜇 = 26 and 𝜎 = 5. (a) Find the z score corresponding to x = 21. (b) Find the z score corresponding to x = 40. (c) Find the raw sc

Algebra ->  Probability-and-statistics -> SOLUTION: A normal distribution has 𝜇 = 26 and 𝜎 = 5. (a) Find the z score corresponding to x = 21. (b) Find the z score corresponding to x = 40. (c) Find the raw sc      Log On


   

Question 1197223: A normal distribution has 𝜇 = 26 and 𝜎 = 5.
(a) Find the z score corresponding to
x = 21.


(b) Find the z score corresponding to
x = 40.


(c) Find the raw score corresponding to
z = −2.


(d) Find the raw score corresponding to
z = 1.1.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

(a)

z+=+%28x-mu%29%2F%28sigma%29
Plug in x+=+21, mu+=+26 and sigma+=+5. Compute to find z.
z+=+%2821-26%29%2F%285%29

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

z+=+-1

The z score is z+=+-1


(b)

Find the z+ score corresponding to x+=+40.
z+=+%2840-26%29%2F%285%29

z+=+14%2F5

z+=+2.8

The z score is z+=+2.8

(c)

Find the raw score corresponding to z+=+-2.
-2+=+%28x+-+26%29+%2F+5
-10+=+x+-+26
26-10=x
x=16


(d) Find the raw score corresponding to z+=+1.1.

1.1+=+%28x+-+26%29+%2F+5
5.5=+x+-+26
26%2B5.5=x
x=31.5