Your local grocery store sells 5 lb bags of potatoes. However, the 5 lb bags don

Question

Your local grocery store sells 5 lb bags of potatoes. However, the 5 lb bags don't weight exactly 5 lbs. If we let X_i be the weight of a randomly selected 5 lb bag of potatoes, historical data indicates that X_i ~ N (5.36, 0.14). The local warehouse store sells 10 lb bags of potatoes, which also do not weight exactly 10 lbs. If Y is the weight of a randomly selected 10 lb bag, historical data indicates that Y ~ N (10.22, 0.18). If we randomly select two 5 lb bags of potatoes and one 10 lb bag of potatoes, what is the probability that the sum of the weights of the two 5 lb bags exceeds the weight of one 10 lb bag?

Explanation / Answer

here let 5 lb baf is 1 and 10 lb bag is 2

hence mean of Y-2X =10.22-2*5.36 =-0.5

and std deviation of Y-2X =(0.18+4*0.14)1/2 =0.8602

hence P(Y-2X<0)=P(Z<(0-(-0.5)/0.8602)=P(Z<0.5812)=0.7195

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