Question

Consider a set of data in which the sample mean is 27 27 and the sample standard deviation is 6.2 6.2 . calculate the z-score given that x=28.5 x = 28.5 . round your answer to two decimal places.

Answer 1

The z-score is calculated using the formula Z = (X - μ) / σ. For an x value of 28.5, with a mean of 27 and a standard deviation of 6.2, the z-score is 0.24 after rounding to two decimal places.

Step-by-step explanation:

To calculate the z-score for an x value of 28.5, with a sample mean of 27 and a sample standard deviation of 6.2, we can use the z-score formula:

Z = (X - μ) / σ

where:

• Z is the z-score
• X is the value for which we want to find the z-score
• μ (mu) is the mean of the data set
• σ (sigma) is the standard deviation of the data set

Substituting the given values, we get:

Z = (28.5 - 27) / 6.2 = 1.5 / 6.2 = 0.241935 (rounded to six decimal places)

Therefore, the z-score, rounded to two decimal places, is 0.24.