Answer Happy

I don't quite understand question e). I know that the negativebinomial should be the sum of (from z=30 to 100)combination(z-1,r-1)*p^r*(1-p)^(z-r) but can't get it to a form ofa binomial.
Question 2 (8 marks) A fruit growing company claims that only 10% of their mangos are bad. They sell the mangos in boxes of 100. Let X be the number of bad mangos in a box of 100. (a) What is the distribution of X and the value(s) of its parameter(s)? (b) Before a grocer will buy a box of 100 mangos, 5 are randomly selected for inspection. Let Y be the number of bad mangos in the batch of 5. Assuming that exactly 10% of the mangos in the box are bad, what is the distribution of Y and the value(s) of its parameter(s)? (c) A box of mangos is rejected if more than one mango in the batch of 5 is found to be bad. Write down the expression for the probability of the inspector rejecting the whole box. No final numerical answer is required. (d) The probability of the inspector rejecting a box is 0.08 (this is the numerical answer for Part (c) to two decimal places). Let Z be the number of boxes inspected until four boxes are rejected. What is the distribution of Z and the value(s) of its parameter(s)? (e) Write down an expression for P(Z > 30) in terms of the probabilities of an appropriate binomial distribution Wb(n, p) stating the values of the parameters n and p. No final numerical answer is required.