The heights of all the 12-year-old boys in the united states are normally distributed with a mean of 59 inches and a standard deviation of 3 inches. what is the probability that a boy chosen randomly from that age group will have a height greater than 65 inches?

65 inches is 2 standard deviations away from the mean (59 + 3 + 3 = 65).  In a normal distribution, 95% of data falls within 2 standard deviations from the mean.  The remaining for the tails would be 100-95=5%.  This would include both tails, however.  We just want the upper level, so we divide by 2:  5/2 = 2.5%.  The probability is 2.5% or 0.025.

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