Question

Deandre finishes a marathon in 245.1 minutes. among all men in the race, the mean finishing time was 253 minutes with a standard deviation of 9.2 minutes. maria finishes the same marathon in 274.2 minutes. among all women in the race, the mean finishing time was 282 minutes with a standard deviation of 7.8 minutes.

(a) compute the z-score for deandre.
(b) compute the z-score for maria.
(c) who did better in the marathon in relation to their gender? briefly explain.

Answer 1

Deandre's z-score is -0.824 and Maria's z-score is -0.923. Deandre performed better compared to the men's average time, while Maria performed better compared to the women's average time.

Step-by-step explanation:

(a) Computing the z-score for Deandre:

1. First, we need to calculate the z-score formula:
2. Z = (X - μ) / σ
3. Where X is the individual score, μ is the population mean, and σ is the population standard deviation.
4. Since Deandre's finishing time is 245.1 minutes, his z-score formula becomes:
   Z = (245.1 - 253) / 9.2
5. Simplifying the equation:
   Z = -0.824

(b) Computing the z-score for Maria:

1. Using the same formula, Maria's z-score is:
   Z = (274.2 - 282) / 7.8
2. Simplifying the equation:
   Z = -0.923

(c) Determining who did better in relation to their gender:

1. In terms of z-scores, a lower z-score indicates a better performance relative to the mean.
2. Since Deandre's z-score is -0.824 and Maria's z-score is -0.923, it means Deandre performed better compared to the men's average time, while Maria performed better compared to the women's average time.