2 . This question aims at investigating the weights of apples and oranges in a food shop .
Apples and oranges are available in a food shop . The weights of apples can be modelled by a normal distribution with mean 100 g and variance
2 10 g , and the weights of oranges can be modelled by a normal distribution with mean
� g and variance
2
6g .
( a ) One apple and two oranges are randomly selected . Let � � 120.
( i ) Write down the mean of the total weight .
( ii ) Write down the variance of the total weight .
( iii ) Hence , find the probability that the total weight of one apple and two oranges is between 321g and 337 g .
( b ) Let � � 125 and D represents the weight of four randomly selected apples subtracted by the triple of the weight of a randomly selected orange . It is given that
2
D ~ N ( m, k ) .
[ 4 ]
( i ) Write down m .
( ii ) Write down the exact value of k .
( iii ) Hence , find the probability that the weight of four randomly selected apples is less than three times the weight of a randomly selected orange .
[ 5 ]
Kylian and Lucy are staffs in the food shop . Kylian wants to conduct a hypothesis test at a 5 % significance level to test whether the population mean weight of oranges is less than 120 g .
Kylian selected 20 oranges randomly to form a sample such that the sample mean weight is 119 g .
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