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.
