Question

heights of children entering kindergarten are normally distributed with a mean height of 103 cm and a standard deviation of 1.27 cm. 67% of the children entering kindergarten are taller than:

Answer 1

In order to find the height at which 67% of children entering kindergarten are taller, we need to find the height at which 33% of children are shorter. Using the z-score formula, we can determine that approximately 102.59 cm is the height at which 67% of children are taller.

Step-by-step explanation:

In order to find the height at which 67% of children entering kindergarten are taller, we need to find the height at which 33% of children are shorter. Since heights are normally distributed, we can use the z-score formula to find this value.

The z-score formula is:

z = (x - mean) / standard deviation

Substituting the given values, we have:

0.33 = (x - 103) / 1.27

Solving for x, we find:

x ≈ 103 - 0.33 * 1.27 ≈ 102.59 cm

Therefore, 67% of the children entering kindergarten are taller than approximately 102.59 cm.