Question

The mean of a set of data is -2.91 and its standard deviation is 3.88. Find the z-score for a value of 2.80.

a) -1.45
b) 1.45
c) -0.95
d) 0.95

Answer 1

To find the z-score for the value of 2.80 with the given mean and standard deviation, apply the formula z = (X - μ) / σ, which yields approximately 1.47. The closest answer choice is 1.45 (option b).

Step-by-step explanation:

The question asks for the calculation of a z-score for a given value (2.80) using the mean (-2.91) and the standard deviation (3.88) of a dataset. To find the z-score, you use the formula:

z = (X - μ) / σ

Where 'X' is the value we want to find the z-score for, 'μ' (mu) is the mean, and 'σ' (sigma) is the standard deviation. Plugging in the values, we get:

z = (2.80 - (-2.91)) / 3.88 = 5.71 / 3.88 ≈ 1.47

The closest answer choice to 1.47 is 1.45, so the correct answer is (b) 1.45.