Analysis and Approaches for IBDP Maths Ebook 1 | Page 295

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2. A company produces containers of milk soda. The volume of milk soda in the containers
is normally distributed with a mean of 350 ml and standard deviation of 6 ml.
A container which contains less than 335 ml of milk soda is unsatisfied.
(a)
A container is selected at random.
(i)
Find the probability that this container is unsatisfied.
(b)
(c)
(ii)
Given that this container is unsatisfied, find the probability that it contains
more than 330 ml of milk soda.
Two containers are selected at random. Find the probability that only one of them
is unsatisfied.
[3]
60 containers are selected at random.
[6]
(i)
(ii)
Find the expected number of these containers that are unsatisfied.
Find the probability that less than 3 of these containers are unsatisfied.
[6]
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)
(b)
(c)
A nail is randomly selected.
(i) Find t .
(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 .
21
(ii)
Find the probability that at least 4 of these nails are short.
[6]
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