,1. A researcher is investigating the number of female cubs present in litters of size 4 He
believes that the number of female cubs in a litter can be modelled by B(4, 0.5) He
randomly selects 100 litters each of size 4 and records the number of female cubs.
The results are recorded in the table below.
Number of female cubs 0 1 2 3 4
Observed number of litters 10 33 33 15 9
He calculated the expected frequencies as follows
Number of female cubs 0 1 2 3 4
Expected number of litters 6.25 r s r 6.25
(a) Find the value of r and the value of s
(3)
(b) Carry out a suitable test, at the 5% level of significance, to determine whether or not
the number of female cubs in a litter can be modelled by B(4, 0.5)
You should clearly state your hypotheses and the critical value used.
(6)
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, 2. The discrete random variable X has probability distribution
x –5 –1 0 5 b
P(X = x) 0.3 0.25 0.1 0.15 0.2
where b is a constant and b > 5
(a) Find E(X ) in terms of b
(1)
Given that Var(X ) = 34.26
(b) find the value of b
(4)
(c) Find P(X 2 < 2 – 3X )
(4)
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*P69194A0424*
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