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Sample Z-Score and Standard ErrorSuppose the population has a mean of 350 and a standard deviation of 90, and you get a sample mean of 370.16 for a sample size of 36, what will be the sample z-score?9.721.34153.83

Question

Sample Z-Score and Standard ErrorSuppose the population has a mean of 350 and a standard deviation of 90, and you get a sample mean of 370.16 for a sample size of 36, what will be the sample z-score?9.721.34153.83

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Solution

To calculate the sample z-score, you can use the formula:

Z = (X - μ) / (σ/√n)

where:

  • X is the sample mean
  • μ is the population mean
  • σ is the standard deviation of the population
  • n is the sample size

Given:

  • X = 370.16
  • μ = 350
  • σ = 90
  • n = 36

Substitute these values into the formula:

Z = (370.16 - 350) / (90/√36)

Simplify the denominator:

Z = (370.16 - 350) / (90/6)

Subtract the means:

Z = 20.16 / 15

Finally, divide to find the z-score:

Z = 1.34

So, the sample z-score is 1.34.

This problem has been solved

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