24 7. The weights of a particular type of apple, A grams, and a particular type of orange, R grams, each follow independent normal distributions. A ~ N(160, 122) R ~ N(140, 102) (a) Find the distribution of (i) A + R (ii) the total weight of 2 randomly selected apples. (3) A box contains 4 apples and 1 orange only. Jesse selects 2 pieces of fruit at random from the box. (b) Find the probability that the total weight of the 2 pieces of fruit exceeds 310 grams. (3) From a large number of apples and oranges, Celeste selects m apples and 1 orange at random. The random variable W is given by W = Ai i m =∑ 1 − n × R where n is a positive integer. Given that the middle 95% of the distribution of W lies between 1100.08 and 1499.92 grams, (c) find the value of m and the value of n (8) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________
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This question is part of the UK A-Level Mathematics syllabus. In the actual exam, structured questions typically require linking specific keywords to gain full marks. Applaa helps you drill these topics.
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