Research shows that 17% of children are absent from school on at least five days during winter because of ill health. A random sample of 55 children is taken.

a. Find the probability that exactly 10 of the children in the sample are absent from school on at least five days during winter because of ill health.

b. Use a suitable approximation to find the probability that at most seven children in the sample are absent from school on at least 5 days during winter because of ill health.

c. Justify the approximation made in part b.