Final answer:
The interval of heights that represents the middle 95% of male heights from this all boys school is between 63 inches and 75 inches.
Step-by-step explanation:
To determine the interval of heights that represents the middle 95% of male heights from this all boys school, we can use the empirical rule. According to the empirical rule, for a normal distribution, approximately 68% of the data falls within 1 standard deviation of the mean, 95% falls within 2 standard deviations, and 99.7% falls within 3 standard deviations.
In this case, the mean height is 69 inches and the standard deviation is 3 inches. So, within 2 standard deviations of the mean, we expect to find the middle 95% of the data. Calculating the interval:
Lower bound = mean - 2 * standard deviation = 69 - 2 * 3 = 63 inches
Upper bound = mean + 2 * standard deviation = 69 + 2 * 3 = 75 inches
Therefore, the interval of heights that represents the middle 95% of male heights from this all boys school is between 63 inches and 75 inches.