Question

The amount of time it takes to see a doctor a CPT-Memorial is normally distributed with a mean of 33 minutes and a standard deviation of 12 minutes. What is the Z-score for a 42 minute wait?
Use the following information to find the Z- score.



⎯⎯⎯⎯⎯
X
¯
⎯⎯⎯⎯⎯
X
¯
= 82


μ

μ
= 89


σ

σ
= 1

n = 22





Round your answer to two decimal places.





Round your answer to two decimal places.

Answer 1

Answer:

a) Z-score = 0.75

b) Z-score = -32.833

Step-by-step explanation:

Step(i):-

Given that mean of the Population = 33

Given a standard deviation of the Population = 12

Let 'X' be a random variable in a normal distribution

Let 'X' = 42

Step(ii):-

     $Z = \frac{x-mean}{S.D}$

    $Z = \frac{42-33}{12} = 0.75$

Step(iii):-

Given that mean of the Population = 89

Given a standard deviation of the Population = 1

Let 'X' be a random variable in a normal distribution

Let 'X⁻ = 82

  $Z = \frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } }$

    $Z = \frac{82-89}{\frac{1}{\sqrt{22} } } = -32.833$

Z-score = -32.833