Question

Consider a set of data in which the sample mean is 33 and the sample standard deviation is 7.3 . Calculate the z-score given that x = 30.4 . Round your answer to two decimal places.

Answer 1

The z-score is calculated by subtracting the mean from the value and then dividing by the standard deviation. In this case, the z-score for x = 30.4 with a mean of 33 and a standard deviation of 7.3 is -0.36.

Step-by-step explanation:

To calculate the z-score for the given value x = 30.4 with a sample mean (μ) of 33 and a sample standard deviation (s) of 7.3, you use the formula:

z = (x - μ) / s

Plugging in the numbers:

z = (30.4 - 33) / 7.3

z = -2.6 / 7.3

z = -0.3562...

Rounded to two decimal places, the z-score is -0.36.

The z-score tells you how many standard deviations an element x is from the mean. In this case, a z-score of -0.36 indicates that 30.4 is less than one standard deviation below the mean.