Question

To qualify for special training, athletes are tested for endurance.

The scores are normally distributed with a mean of 840 and a standard
deviation of 89. If only the top 15% of the athletes are selected, what would
the cutoff score be?

Answer 1

The cutoff score for the top 15% of athletes is approximately 933.

Explanation:

To find the z-score for the top 15%, we need to find the z-score that corresponds to a cumulative probability of 0.85 (since we want the top 15%, which is the same as the highest 85%). Using a standard normal distribution table or calculator, we can find that the z-score corresponding to a cumulative probability of 0.85 is approximately 1.04.

Now we can use the z-score formula to solve for the cutoff score:

z = (x - μ) / σ

1.04 = (x - 840) / 89

Multiplying both sides by 89, we get:

93 = x - 840

Adding 840 to both sides, we get:

x = 933

Therefore, the cutoff score for the top 15% of athletes is approximately 933.