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1 answer:
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Answer:
a) 3354 seconds
b) 6294 seconds
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
(a) The cutoff time for the fastest 5% of athletes in the men's group, i.e. those who took the shortest 5% of time to finish.
The cutoff for the shortest 5% is the 5th percentile, which is X when Z has a pvalue of 0.05. So X when Z = -1.645.
Cutoff of 3354 seconds.
(b) The cutoff time for the slowest 10% of athletes in the women's group.
The slowest 10% is the 10% that takes more time, so the cutoff is the 100 - 10 = 90th percentile, which is X when Z has a pvalue of 0.9. So X when Z = 1.28.
Cutoff time of 6294 seconds