Final answer:
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.