Kathy and her brother Clay recently ran in a local marathon. The distribution of finishing time for women was approximately normal with mean 259 minutes and standard deviation 32 minutes. The distribution of finishing time for men was approximately normal with mean 242 minutes and standard deviation 29 minutes. (a) The finishing time for Clay was 289 minutes. Calculate and interpret the standardized score for Clay’s marathon time. Show your work.

His standardized score was Z = 1.62. This means that his finishing time is 1.62 standard deviations above the finishing time for men in the local marathon.

Step-by-step explanation:

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.

The distribution of finishing time for men was approximately normal with mean 242 minutes and standard deviation 29 minutes.

This means that

(a) The finishing time for Clay was 289 minutes. Calculate and interpret the standardized score for Clay’s marathon time. Show your work.

This is Z when X = 289.

His standardized score was Z = 1.62. This means that his finishing time is 1.62 standard deviations above the finishing time for men in the local marathon.

452,489 to the nearest thousand is 452,000