A) A retail grocery merchant figures that her daily gain X from sales is a norma

Question

A) A retail grocery merchant figures that her daily gain X from sales is a normally distributed random variable with = 70 and = 4 (measurements in dollars). X can be negative if she is forced to dispose of enough perishable goods. Also, she figures daily overhead costs Y to have a gamma distribution with = 5 and = 2. If X and Yare independent, find the expected value and variance of her net daily gain.

expected value $ -

variance -  

B) Would you expect her net gain for tomorrow to rise above $100?

-No, because $100 is more than 3 standard deviations above the expected value, which makes it unlikely.

-Yes, because $100 is more than 3 standard deviations above the expected value, which makes it likely.

-No, because $100 is less than 3 standard deviations above the expected value, which makes it unlikely

-Yes, because $100 is less than 3 standard deviations above the expected value, which makes it likely.

Explanation / Answer

A) here expected value of net gain =E(X)-E(Y) =70- =70-5*2 =60

an variance =Var(X)+Var(Y) =42+2 =16+5*22 =36

B) std deviation =(36)1/2 =6

therefore 100 is more than 3 std deviaiton above expected value. hence correct option is :

-No, because $100 is more than 3 standard deviations above the expected value, which makes it unlikely.

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