MJC Prelim 9740/2014/02/Q10

MJC Prelim 2014 Paper 2 Question 10

The masses, in kilograms, for a randomly chosen pumpkin and a randomly chosen watermelon, are normally distributed with means 4.2 and 8.5, and standard deviations 1.6 and 2.2 respectively.

(i) Find the range of values of k such that the average mass of five randomly chosen watermelons exceeds k kilograms occurs at most 10% of the time

(ii) Find the probability that total mass of five randomly chosen pumpkins differs from three times the average mass of five randomly chosen watermelons by more than 5 kg.

(iii) A fruit store has 70 batches, each consisting of n pumpkins. It is known that, on average, 3 in 20 pumpkins are rotten. Given that in the 70 batches, the probability of having an average of at least 4 rotten pumpkins per batch is more than 0.7. Determine the minimum value of n.