If the value of a characteristic of a population is normally distributed, the probability distribution is such that has a bell shaped curved that has a highest probability at the mean and decreases uniformly in both directions. One of the characteristics if the normal distribution curve is that approximately 68% of the values lie within one standard deviation of the mean.

Here, the population is normally distributed with a mean of 100 and a standard deviation of 15.

The probability of a sample of three having a mean of 115 or more is approximately 16%. Whether you consider this unusual or not is dependent or your degree of tolerance.

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