I had hard to time with this question - first it took me more than 3 minutes just the read the text as I could not comprehend it....Then I had difficulties with percentiles...I had it wrong for the third question. Official explanations are:
Using Height-for-age standards for boys aged 4 years 0 months, the 15th percentile in height is 99.0 cm. Thus, 15% of boys of this age are 99.0 cm tall or shorter. Note that the 3rd percentile in height for boys of this age is 95.4 cm, so 3% of boys of this age are at this height or shorter. Therefore, (15 − 3)%, or 12% of boys aged 4 years 0 months have heights greater than 95.4 cm and less than or equal to 99.0 cm. The proportion of boys of this age whose height is exactly 99.0 cm must therefore be less than or equal to 12%, so the indicated probability is also less than or equal to 12%.
The correct answer is No.
Using Height-for-age standards, the 3rd percentile in height for ages from 2 years 0 months through 5 years 0 months is at least 81.4 cm. This means that a boy from a model population whose height is 81.4 cm is shorter than at least 97% of boys his age. Thus, a boy who is 81 cm tall is shorter than at least 97% of boys his age and thus shorter than at least 95% of boys his age.
The correct answer is Yes.
Weight-for-height standards provide a weight distribution for boys 120 cm tall; in particular, 97% of boys at this height weigh more than 18 kg. But a randomly selected boy at this height could conceivably weigh much less than 18 kg. Moreover, even if the boy's weight were known, a percentile distribution of weight for boys age 2 years 6 months is lacking, so it is impossible to answer the question based on the information provided.
The correct answer is No.