Apps. and Interpretation for IBDP Maths Ebook 1 | Page 313

Exercise 89
1. The weights of fish in a lake are normally distributed with a mean of 740 g and standard
deviation 46 g. Fishes are classified as big fishes if they are heavier than 850 g.
(a)
A fish is randomly selected from the lake.
(i)
Find the probability that this fish is big.
(b)
(c)
(ii) Given that this fish is big, find the probability that it is heavier than 900 g.
[6]
Two fishes are randomly selected. Find the probability that they are both big.
[2]
100 fishes are randomly selected.
(i)
(ii)
Find the expected number of these fishes that are big.
Find the probability that more than 2 of these fishes are big.
[6]
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.
21
(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.
[6]
Two containers are selected at random. Find the probability that only one of them
is unsatisfied.
[3]
60 containers are selected at random.
(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]
www.seprodstore.com
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