Apps. and Interpretation for IBDP Maths Ebook 2 | Page 300

Your Practice Set – Applications and Interpretation for IBDP Mathematics

Consider the following table :

X ~ B ( 100 , 0.03 ) P ( 0 � X � 4 ) 0.8178548035 P ( X � 5 ) 0.101308065 P ( X � 6 ) 0.0496096195 P ( X � 7 ) 0.0206037006

P ( 8 � X � 100 ) 0.0106238089

( ii ) Hence , write down the greatest value of n such that the null hypothesis of the test is not rejected .

[ 3 ]

4 . The number of online transactions per day follows a Poisson distribution with mean � . It is found that there are n online transactions on a particular day .

A hypothesis test is conducted at a 1 % significance level to test whether � is greater than 2.5 .

( a ) ( i ) Write down the null hypothesis of the test .

( ii ) Write down the alternative hypothesis of the test .

Consider the following table :

[ 2 ]

X ~ Po ( 2.5 ) P ( 0 � X � 5 ) 0.9579789618 P ( X � 6 ) 0.0278337262 P ( X � 7 ) 0.0099406165 P ( X � 8 ) 0.0031064427 P ( X � 9 ) 0.0011402528

( ii ) Hence , write down the greatest value of n such that the null hypothesis of the test is not rejected .

[ 3 ]

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