Mathematics 9709 · AS & A Level · Continuous random variables

Continuous random variables — practice question

The masses of apples sold by a store may be represented by a normal distribution with mean $120$ grams and standard deviation $24$ grams. Apples with weight below $90$ grams are labelled ‘small’; apples with weight above $140$ grams are labelled ‘large’; all others are labelled ‘medium’.
(i)[4]

Show that the chance that an apple selected at random is graded as medium is $0.692$, correct to $3$ significant figures.

(ii)[4]

Four apples are picked at random. Find the probability that at least two of them are graded as medium.

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