Your Practice Set – Applications and Interpretation for IBDP Mathematics
Exercise 62
1 . The number of goals scored in a randomly selected match by a football team follows a Poisson distribution with mean 1.7 .
( a ) Find the probability that less than two goals are scored in a particular match .
( b ) Find the probability that exactly ten goals are scored in six randomly selected matches .
( c ) Given that in six randomly selected matches less than nine goals are scored , find the probability that less than six goals are scored .
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[ 2 ]
[ 3 ]
2 . In a hotline centre , the number of incoming calls is distributed as Poisson with mean 12.8 in a 30-minute time period .
( a ) Find the probability that more than 10 incoming calls are received in a particular 30-minute time period .
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( b ) Find the probability that at most 33 incoming calls are received in a particular 90-minute time period .
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( c ) Given that a particular 90-minute time period at least 40 incoming calls are received , find the probability that exactly 43 incoming calls are received .
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3 . The number of delays in a day of a railway system follows a Poisson distribution with mean 3.1 .
( a ) Find the probability that there are at least 2 delays in a day . [ 2 ]
( b ) Find the probability that there are at most 28 delays in a week . [ 2 ]
( c ) Find the probability that in 7 consecutive days there are at most 4 delays in each day .
[ 2 ]
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