The wildlife conservation group is interested in the health of reproducing female wallabies. The wildlife group has established that 83% of female wallabies have a joey in their pouch. The group also know that 68% of wallabies in the region are female. You may assume that the sex and joey status of wallabies are independent wallaby to wallaby.
a) Use an appropriate limiting distributio to estimate the probability that at least 600 wallabies from a sample of 1000 have a joey.
b) From birth, joeys spend an average of 280 days in their mothers pouch. To answer the following, you may assume that the time a joey spends in the pouch is exponentially distributed.