The 400-meter race times recorded in the boys track meet was normally distributed with a standard deviation of 3 seconds. If David finished the race in 51.2 seconds with a z-score of -2.6, what is the mean time?

The mean time is 59 seconds.

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 question, we have that:

If David finished the race in 51.2 seconds with a z-score of -2.6, what is the mean time?

This means that when X = 51.2, Z = -2.6. So

The mean time is 59 seconds.

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step-by-step explanation: