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junior college 1 | H1 Maths

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I got 199 for (i)

How can I do part (ii) and (iii)?

Part (ii), I tried as follows:

X - B(200, 0.97)

P(X =< 199) =

I was not able to get the answer.

Help is needed. Thanks.

205 tickets were sold, so no. of trials is 205, not 200.

... should be X~B(205,0.97).

since flight can hold 200 passengers, then total passengers that show up cannot exceed 200.

P(all show up can take flight)

= P(X<=200)

= 0.738681

(iii)

E(X) = np = 205x0.97 = 198.85

P(X>198.85 | X<=200)

= [P(X=199)+P(X=200)] / P(X<=200)

= (0.162715+0.157833) / 0.738681

= 0.433947

for (i), just to clarify ...

most probable number & expected number are not the same thing.

from GC ...

P(X=197) = 0.1095

P(X=198) = 0.1431

P(X=199) = 0.1627

P(X=200) = 0.1578

P(X=201)= 0.1269

since P(X=199) has highest probability, so most probable number of passengers is 199, whereas expected number is 198.85 .

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