2018 ASRJC P2 Q6

A jackfruit farm produces \(2\) types of jackfruit pulps namely Grade \(\mathrm{A}\) and Grade \(\mathrm{B}\). The pulps are randomly packed into boxes of \(8\).

The probability that a box contains at most \(3\) Grade \(\mathrm{A}\) jackfruit pulps is \(0.00245\).

A fruit trading wholesaler places a monthly order of \(1000\) boxes of jackfruit pulps for \(5\) years.

Find the approximate probability that the mean number of boxes that contains at most \(3\) Grade \(\mathrm{A}\) jackfruit pulps in a month is more than \(3\).

[You may assume that there are \(12\) months in a year.]