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ozzi
3 years ago
13

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 devi

ation 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.
Mathematics
1 answer:
Eva8 [605]3 years ago
7 0

Answer:

a) <em>Z-score = 0.75</em>

b) <em>Z-score = -32.833</em>

Step-by-step explanation:

<u><em>Step(i):-</em></u>

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

<u><em>Step(ii):-</em></u>

<em>      </em>Z = \frac{x-mean}{S.D}<em></em>

<em>     </em>Z = \frac{42-33}{12} = 0.75<em></em>

<u><em>Step(iii):-</em></u>

<em>Given that mean of the Population = 89</em>

Given a standard deviation of the Population = 1

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

Let 'X⁻ = 82

<em>   </em>Z = \frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } }<em></em>

<em>     </em>Z = \frac{82-89}{\frac{1}{\sqrt{22} } } =  -32.833<em></em>

<em>Z-score = -32.833</em>

<em></em>

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