In two shipments of fruit, A and B, the proportions of fruit that are apples are and , respectively. Suppose that independent random samples of 50 fruit from A and 100 fruit from B. Let be the sample proportion of apples from shipment A and be the sample proportion of apples from shipment B. What is the mean of the sampling distribution of -

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In two shipments of fruit, A and B, the proportions of fruit that are apples are and , respectively. Suppose that independent random samples of 50 fruit from A and 100 fruit from B. Let  be the sample proportion of apples from shipment A and be the sample proportion of apples from shipment B. What is the mean of the sampling distribution of -  ?

the mean of the sampling distribution is -  

Step-by-step explanation:

Given the data in the question;

let be number of apples from the shipment A

and be number of apples from shipment B

 =   /    =   / 50                             {  x ¬ Bin(np )

{ = 50  )

 =   /    =   / 100

( = 100 )

E( -  ) = E( /    - /   )

= E( / 50  -   / 100 )

= E() / 50  -  E() / 100

= 50 / 50  -  100  / 100

=   -             { E(X) = np ]

Therefore, the mean of the sampling distribution is -  

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step-by-step explanation: