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When Stephan moved from Illinois to Florida, his average monthly electric bill increased from $83 to $102. He is curious to know whether his IL or FL electric bill is relatively more or less expensive, when compared to the distribution of electric bills for each state. In Illinois, the mean monthly electric bill is $85, with a standard deviation of $3.20. In Florida, the mean monthly electric bill is $105, with a standard deviation of $4.00. Compute the z-scores for Stephan's IL and FL electric bills. Round to three decimal places if necessary.

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JeanaShupp

Answer: The z-scores for Stephan's IL and FL electric bills. are -0.625 and 0.75 respectively.

Step-by-step explanation:

Given:  Average monthly electric bill in Illinois =  $83

Average monthly electric bill in Florida = $102

Formula of z : [tex]z=\dfrac{X-mean}{standard\ deviaton}[/tex]

In Illinois, the mean monthly electric bill is $85, with a standard deviation of $3.20.

[tex]z=\dfrac{83-85}{3.20}= -0.625[/tex]

In Florida, the mean monthly electric bill is $105, with a standard deviation of $4.00.

[tex]z=\dfrac{105-102}{4}=\dfrac{3}{4}=0.75[/tex]

Hence, the z-scores for Stephan's IL and FL electric bills. are -0.625 and 0.75 respectively.

Using it's formula, it is found that the z-scores are:

  • For Illinois, of Z = -0.625.
  • For Florida, of Z = -0.75.
  • Due to the lower z-score, the bill is relatively lower in Florida.

Z-score:

In a distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

  • It measures how many standard deviations the measure is from the mean.  
  • The higher z-score means that the measure X is relatively higher.

In Illinois:

  • Bill of $83, mean of $85, standard deviation of $3.2, hence [tex]X = 83, \mu = 85, \sigma = 3.2[/tex]

Then:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{83 - 85}{3.2}[/tex]

[tex]Z = -0.625[/tex]

In Florida:

  • Bill of $102, mean of $105, standard deviation of $4, hence [tex]X = 102, \mu = 105, \sigma = 4[/tex]

Then:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{102 - 105}{4}[/tex]

[tex]Z = -0.75[/tex]

Due to the lower z-score, the bill is relatively lower in Florida.

To learn more about z-scores, you can take a look at https://brainly.com/question/21620274

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