Analysis and Approaches for IBDP Maths Ebook 1 | Page 296

Your Practice Set – Analysis and Approaches for IBDP Mathematics
4. The masses of watermelons grown on a farm are normally distributed with a mean of
9 kg and standard deviation 0.4 kg.
A watermelon is large if its mass is greater than t kg. Ten percent of the watermelons are
classified as large.
(a)
A watermelon is selected at random.
(i) Find t .
(b)
(c)
(ii)
Given that this watermelon is large, find the probability that it is less than
9.8 kg.
Three watermelons are selected at random. Find the probability that they are all
large.
52 watermelons are selected at random. Let X be the number of large
watermelons in this sample.
[6]
[2]
(i) Find the variance of X .
(ii)
Find the probability that at least 13 and at most 26 of these watermelons
are large.
[6]
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