The Palestinian Central Bureau of Statistics (www.pcbs.gov.ps) asked mothers of age 20-24 about the ideal number of children. For those living on the Gaza Strip, the probability distribution is approximately P(1) = 0.01, P(2) = 0.10, P(3) = 0.09, P(4) = 0.31, P(5) = 0.19, and P(6 or more) = 0.29.

(a) Because the last category is open ended, it is not possible to calculate the mean exactly. Find a lower bound for the mean.

(b) Explain why you can find the median of the distribution, and find it.