Question

Given the mean of 100 and the standard deviation of 5.3, what is the z-score for 130?

a) 5.66
b) 5.47
c) 5.09
d) 4.91

Answer 1

The z-score for a score of 130 with a mean of 100 and a standard deviation of 5.3 is approximately 5.66, which corresponds to option a).

Step-by-step explanation:

To calculate the z-score for a score of 130, we use the formula z = (X - μ) / σ, where X is the value in the data set, μ (mu) is the mean, and σ (sigma) is the standard deviation. Given the mean is 100 and the standard deviation is 5.3, we can plug in the values:

z = (130 - 100) / 5.3

= 30 / 5.3

≈ 5.66

Therefore, the z-score for a score of 130 with this data set is approximately 5.66, which corresponds to option a).