A greengrocer displays apples in trays. Each customer selects the apples he or she wishes to buy and puts them into a bag.
Records show that the weight of such bags of apples may be modelled by a normal distribution with mean 1.16 kg and standard deviation 0.43 kg .
Determine the probability that the mean weight of a random sample of 10 such bags of apples exceeds 1.25 kg .
The greengrocer also displays pears in trays. Each customer selects the pears he or she wishes to buy and puts them into a bag.
A random sample of 40 such bags of pears had a mean weight of 0.86 kg and a standard deviation of 0.65 kg .
Construct a \(\mathbf { 9 6 \% }\) confidence interval for the mean weight of a bag of pears.
Hence comment on a claim that customers wish to buy, on average, a greater weight of apples than of pears. [0pt]
[2 marks]