The distances male long jumpers for State College jump are approximately normal with a mean of 263 inches and a standard deviation of 14 inches. Suppose a male long jumper's jump is ranked in the 75th percentile. How long was his jump?

His jump was of 272.45 inches

Step-by-step explanation:

Problems of normally distributed samples are solved using 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.

In this problem, we have that:

75th percentile

X when Z has a pvalue of 0.75. So X when Z = 0.675

His jump was of 272.45 inches

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step-by-step explanation: