Final answer:
Half of the children are more than 50 cm tall and 75% of the children are less than 25 cm tall.
Step-by-step explanation:
To complete the statement i. Half of the children are more than 50 cm tall. ii. 75% of the children are less than 25 cm tall. To answer the student's question, we have to infer the missing heights in the following statements: i. Half of the children are more than __ cm tall. ii. 75% of the children are less than __ cm tall.
Based on the information given, the 50th percentile corresponds to the value below which 50 percent of individuals fall. This is commonly referred to as the median. Similarly, if 75% are less than a certain height, we are looking for the value associated with the 25th percentile of the height distribution because percentiles indicate the value below which a given percentage of observations fall.
We do not have exact values for these percentiles, so we cannot determine the precise answers. However, we can look at the provided options and use process of elimination. Answer choice A (i. 50; ii. 75) suggests that 50% are more than 50 cm tall, and 75% are less than 75 cm tall. Choice B (i. 75; ii. 25) indicates 50% are more than 75 cm tall and 75% are less than 25 cm tall, which seems reversed. Choice C (i. 25; ii. 75) is the opposite of what is described in the statements. Choice D (i. 50; ii. 25) indicates half are taller than 50 cm and 75% are shorter than 25 cm, which is inconsistent with a standard height distribution.