2 . A company produces containers of milk soda . The volume of milk soda in the containers is normally distributed with a mean of 500 ml and standard deviation of 8 ml . A container which contains less than 490 ml of milk soda is unsatisfied .
( a ) On the following diagram , shade the region representing the probability that a container is unsatisfied .
[ 2 ]
( b ) A container is selected at random . x
( i ) Find the probability that this container is unsatisfied .
( ii ) Given that this container is unsatisfied , find the probability that it contains more than 483 ml of milk soda .
[ 5 ]
( c ) Two containers are selected at random . Find the probability that only one of them is unsatisfied .
[ 3 ]
Ethan randomly bought ten containers from a department store . He has an agreement with his teacher that the teacher needs to pay Ethan $ 10 if none of the containers is unsatisfied ; Ethan needs to pay his teacher $ 5 if one or two containers are unsatisfied , and Ethan needs to pay his teacher $ 20 if more than two containers are unsatisfied .
The above agreement can be summarized in the following table :
The amount that Ethan receives from his teacher |
�
$ 20
|
�
$ 5
|
$ 10 |
Probability |
q |
1� p� q |
p |
( d ) Write down the value of
( i ) p ;
( ii ) q ;
( iii ) the expected amount that Ethan receives from his teacher . [ 6 ]
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