High School

Evaluate [tex] z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}} [/tex] if [tex] \bar{x} = 39.1 [/tex], [tex] \mu = 24.8 [/tex], [tex] \sigma = 7.2 [/tex], and [tex] n = 16 [/tex].

[tex] z = 7.94 [/tex]

(Type an integer or decimal rounded to two decimal places as needed.)

Answer :

The z-score is calculated using the provided values by substituting them into the z-score formula and simplifying the expression. The calculated z-score is 7.94, which is the number of standard deviations the sample mean is from the population mean.

The question is asking to evaluate the z-score formula z = (x - \μ) / (\σ / \\sqrt{n}), where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size. Given the values x= 39.1, μ = 24.8, σ = 7.2, and n = 16, we will use these to calculate the z-score. Following the formula:

  • z = (39.1 - 24.8) / (7.2 / \sqrt{16})
  • z = (14.3) / (7.2 / 4)
  • z = (14.3) / (1.8)
  • z = 7.94

Therefore, the z-score is approximately 7.94, which indicates the number of standard deviations the sample mean is from the population mean. This is a high z-score, suggesting that the sample mean is much greater than the population mean.

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