Standard +0.3 This question requires understanding that peeled banana weight = 0.65 × original weight, then applying normal distribution properties (scaling and linear combinations). Part (a) is straightforward standardization. Part (b) requires combining independent normals (2 peeled bananas + 20 strawberries), which is a standard Further Maths Statistics technique but involves careful arithmetic with means and variances. The conceptual steps are routine for this syllabus level.
2. The weights of bananas sold by a supermarket are modelled by a Normal distribution with mean 205 g and standard deviation 11 g . When a banana is peeled the change in its weight is modelled as being a reduction of \(35 \%\).
a) Find the probability that the weight of a randomly selected peeled banana is at most 150 g .
Andy makes smoothies. Each smoothie is made using 2 peeled bananas and 20 strawberries from the supermarket, all the items being randomly chosen. The weight of a strawberry is modelled by a Normal distribution with mean 22.5 g and standard deviation 2.7 g .
b) Find the probability that the total weight of a smoothie is less than 700 g . [0pt]
2. The weights of bananas sold by a supermarket are modelled by a Normal distribution with mean 205 g and standard deviation 11 g . When a banana is peeled the change in its weight is modelled as being a reduction of $35 \%$.\\
a) Find the probability that the weight of a randomly selected peeled banana is at most 150 g .
Andy makes smoothies. Each smoothie is made using 2 peeled bananas and 20 strawberries from the supermarket, all the items being randomly chosen. The weight of a strawberry is modelled by a Normal distribution with mean 22.5 g and standard deviation 2.7 g .\\
b) Find the probability that the total weight of a smoothie is less than 700 g .\\[0pt]
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\hfill \mbox{\textit{SPS SPS FM Statistics 2021 Q2 [7]}}