A set of elementary school student heights are normally distributed with a mean of 105 centimeters and a standard deviation of 5 centimeters. What proportion of student heights are between 114 centimeters and 118 centimeters? You may round your answer to four decimal places.
i think it would be middle schoolers but the question is confusing.
The proportion of student heights that are between 94.5 and 115.5 is 86.64%
We have a mean and a standard deviation . For a value x we compute the z-score as , so, for x = 94.5 the z-score is (94.5-105)/7 = -1.5, and for x = 115.5 the z-score is (115.5-105)/7 = 1.5. We are looking for P(-1.5 < z < 1.5) = P(z < 1.5) - P(z < -1.5) = 0.9332 - 0.0668 = 0.8664. Therefore, the proportion of student heights that are between 94.5 and 115.5 is 86.64%