Question

The mean number of push-ups done by a group of students was 68 with a standard deviation of 12. If Jane's z-score was -2.25, how many push-ups did she do?

Answer 1

Jane did 41 push-ups, which is calculated by adding her z-score (multiplied by the standard deviation) to the mean number of push-ups.

Step-by-step explanation:

The question asks how many push-ups Jane did based on her z-score in a set of data regarding push-ups completed by a group of students. The mean (average) number of push-ups in the group is 68, with a standard deviation of 12. A z-score represents the number of standard deviations a value is from the mean. Jane's z-score is -2.25, which means she performed 2.25 standard deviations less than the average.

To find the number of push-ups Jane did, we use the formula: X = μ + Zσ,

Where X is the raw score, μ is the mean, Z is the z-score, and σ is the standard deviation.

In this case, the calculation would be: X = 68 + (-2.25)(12) = 68 - 27 = 41.

Therefore, Jane did 41 push-ups.