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A physical fitness association is including the mile run in its high school fitness test. The time for this event is known to possess a normal distribution with a mean of seconds and a standard deviation of seconds. Find the probability that a randomly selected high school student can run the mile in less than seconds. Round to four decimal places.

User Fedj
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Answer:

This probability is the p-value of Z given
Z = (X - \mu)/(\sigma), considering X as less than X seconds,
\mu as the mean and
\sigma as the standard deviation.

Explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean
\mu and standard deviation
\sigma, the z-score of a measure X is given by:


Z = (X - \mu)/(\sigma)

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 p-value, we get the probability that the value of the measure is greater than X.

In this question:

Mean
\mu, standard deviation
\sigma.

Find the probability that a randomly selected high school student can run the mile in less than X seconds.

This probability is the p-value of Z given
Z = (X - \mu)/(\sigma), considering X as less than X seconds,
\mu as the mean and
\sigma as the standard deviation.

User BasZero
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