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

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       Log On


   

Question 1200387: 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 = 1.9.
Answer by math_tutor2020(3817) About Me  (Show Source):
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Answers:
  1. z = -1
  2. z = 2.8
  3. x = 16
  4. x = 35.5

Work Shown:

mu = 𝜇 = 26 = mean
sigma = 𝜎 = 5 = standard deviation

Part (a)
z = (x-mu)/sigma
z = (x-26)/5
z = (21-26)/5
z = -5/5
z = -1

Part (b)
z = (x-mu)/sigma
z = (x-26)/5
z = (40-26)/5
z = 14/5
z = 2.8

Part (c)
z = (x-mu)/sigma
z = (x-26)/5
-2 = (x-26)/5
-2*5 = x-26
-10 = x-26
x = -10+26
x = 16

Part (d)
z = (x-mu)/sigma
z = (x-26)/5
1.9 = (x-26)/5
1.9*5 = x-26
9.5 = x-26
9.5+26 = x
35.5 = x
x = 35.5