Question

According to a brief report by the Australian Institute of Health and Welfare, a child with a head circumstance less than the third percentile is considered to have a condition called microcephaly, which may indicate reduced brain volume.2 (squared) In other words, in a large group of children, roughly 3% of them have such a condition. In this question, consider a group of 50 children randomly selected nationally, and let X represent the number of children among this group who have microcephaly.

(a) Write down the possible values of X.

(b) What is a suitable distribution for X? Explain your answer by showing that the assumption(s) of this distribution is (are) met. For the distribution chosen, you must state the parameter(s) as well.

(c) Manually calculate the probability that there are two children who have microcephaly in the sample.

(d) Manually calculate the probability that there is more than one child with microcephaly in the sample.

Answer 1