Question

A set of elementary school student heights are normally distributed with a mean of 105105105 centimeters and a standard deviation of 777 centimeters. What proportion of student heights are between 94.594.594, point, 5 centimeters and 115.5115.5115, point, 5 centimeters? You may round your answer to four decimal places.

Answer 1

Answer:

The proportion of student heights that are between 94.5 and 115.5 is 86.64%

Step-by-step explanation:

We have a mean $\mu = 105$ and a standard deviation $\sigma = 7$. For a value x we compute the z-score as $(x-\mu)/\sigma$, 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%

Answer 2

Answer:

0.4247

Step-by-step explanation: