Apps. and Interpretation for IBDP Maths Ebook 1 | Page 314

Your Practice Set – Applications and Interpretation for IBDP Mathematics
3. A machine manufactures a large number of nails. The length, L mm, of a nail is
2
normally distributed, where L ~ N(70, 3 ) . There are 15% of the nails which are shorter
than t mm, and they are classified as short nails.
(a)
A nail is randomly selected.
(i) Find t .
(b)
(c)
(ii) Given that this nail is short, find the probability that it is shorter than
65 mm.
[6]
Two nails are randomly selected. Find the probability that only one of them is
short.
[3]
25 nails are randomly selected. Let X be the number of short nails in this sample.
(i) Find the variance of X .
(ii)
Find the probability that at least 4 of these nails are short.
[6]
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.
[6]
Three watermelons are selected at random. Find the probability that they are all
large.
[2]
52 watermelons are selected at random. Let X be the number of large
watermelons in this sample.
(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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