Questions: The mean monthly rent of students at Oxnard University is 970 with a standard deviation of 204. (a) John's rent is 1,390. What is his standardized z-score? (Round your answer to 3 decimal places.)

The mean monthly rent of students at Oxnard University is 970 with a standard deviation of 204. (a) John's rent is 1,390. What is his standardized z-score? (Round your answer to 3 decimal places.)
Transcript text: The mean monthly rent of students at Oxnard University is $\$ 970$ with a standard deviation of $\$ 204$. (a) John's rent is $\$ 1,390$. What is his standardized $z$-score? (Round your answer to 3 decimal places.)
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Solution

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Solution Steps

Step 1: Identify the Given Values

We are given the following values:

  • Mean monthly rent, μ=970\mu = 970
  • Standard deviation, σ=204\sigma = 204
  • John's rent, X=1390X = 1390
Step 2: Calculate the Z-Score

The formula for calculating the standardized zz-score is:

z=Xμσ z = \frac{X - \mu}{\sigma}

Substituting the given values:

z=1390970204=4202042.0588 z = \frac{1390 - 970}{204} = \frac{420}{204} \approx 2.0588

Step 3: Round the Z-Score

Round the zz-score to three decimal places:

z2.059 z \approx 2.059

Final Answer

z2.059\boxed{z \approx 2.059}

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