2 . A coffee shop provides 800 breakfast packages for customers every morning . The weights W g of the packages are normally distributed with mean 390 g and standard deviation 13 g .
( a ) Find the probability that the weight of a randomly chosen package is less than 400 g .
[ 2 ] ( b ) Hence , find the expected number of packages less than 400 g in any morning .
( c ) Given that the weight of a randomly chosen package is less than 400 g , find the probability that its weight is less than 385 g .
The manager of the coffee shop wants to set the prices for the breakfast packages of different ranges of weights , as shown in the following table .
Weight
W g W � j j �W � k W � k
Price $ P $ 4 $ 4.5 $ 5
It is given that 50 % and 20 % of the breakfast packages provided in every morning cost $ 4 and $ 5 respectively .
( d ) ( i ) Write down j .
[ 2 ]
[ 3 ]
( ii ) Write down the percentage of the breakfast packages provided in every morning that costs $ 4.5
( ii ) Find k .
( e ) Hence , find the expected daily income from selling the packages , assuming that all packages can be sold .
[ 4 ]
[ 3 ]
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