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.