Apps. and Interpretation for IBDP Maths Ebook 1 | Page 294

Your Practice Set – Applications and Interpretation for IBDP Mathematics
Exercise 82
1. A fair eight-faced die with numbered faces 1, 2, 3, 4, 5, 6, 7 and 8 is tossed for ten times.
(a) Find the expected number of multiples of 4 landed.
(b) Find the variance of the number of multiples of 4 landed.
(c) Find the probability that the number of multiples of 4 landed is 3.
[2]
[2]
[2]
2. A random variable X follows a binomial distribution such that X ~ B( n , 0.6) , where n
is a positive integer. It is given that the expected value of X is 18.
(a) Find the value of n .
(b) Find the value of Var( X ) .
(c) Find the value of P( X � 19) .
[2]
[2]
[2]
3. A game spinner is produced such that the probability of getting a yellow color is landed is
p , where p � 0.5 . The spinner is tossed for 20 times. It is given that the variance of the
number of yellow color landed is 3.2.
(a) Find the value of p .
[3]
(b) Find the expected number of yellow color landed.
[2]
(c) Find the probability of getting a yellow color for 17 times.
[2]
4. Paul lives in a city. He believes that a proportion p of all n citizens in the city will vote
for him in an election. It is given that the mean and the variance of the number of citizens
voting for Paul are 1800 and 990 respectively.
(a) Find the value of p .
[3]
(b) Find the value of n .
[2]
(c) Write down the probability that only half of all citizens vote for him, giving the
answer in the form
decimal places.
a� 10 k , where 1�a
� 10 and k � , and correct a to 4
[2]
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