Question

A set of elementary school student heights are normally distributed with a mean of 105 centimeters and a standard deviation of 7 centimeters. What proportion of student heights are between 594, point, 5 centimeters and 115 point, 5 centimeters? You may round your answer to four decimal places.

Answer 1

To find the proportion of student heights between 594.5 cm and 115.5 cm, we calculate the z-scores for these values and use a standard normal distribution table to find the proportion of values between these z-scores.

Step-by-step explanation:

In order to find the proportion of student heights between 94.5 cm and 115.5 cm, we need to calculate the z-scores for these values. The formula for calculating the z-score is:

z = (x - mean) / standard deviation

Using this formula, the z-score for a height of 94.5 cm is:

z = (94.5 - 105) / 7 = -1.5

The z-score for a height of 115.5 cm is:

z = (115.5 - 105) / 7 = 1.5

Next, we can use a standard normal distribution table to find the proportion of values between these z-scores. From the table, we can determine that the proportion of values between -1.5 and 1.5 is approximately 0.8664.