A lvl H1 statistics qn

Bigcable22 SG

A supermarket obtains a large supply of apples of a single varitety. The mass of an apple has a normal distribution with mean 0.234kg and standard deviation 0.025kg. Some of the apples are packed at random into "small" bags,each containing 5 apples,and others are packed at random into "large" bags ,each containing 10 apples.

Find the probability that the total mass of two randomly chosen small bags is within +0.2kg/-0.2kg of the mass of a randomly chosen large bag.

Lee buys 2 small bags at $1.50 per kg,and fo buys one large bag at $1.20 per kg.Find the probability that Lee pays at least $0.50 more than Foo.

eagle SG

X ~ N(0.234, 0.025^2)

Small Bag, S ~ N(0.234*5, 0.025^2 * 5)

Large Bag, L ~ N(0.234*10, 0.025^2 * 10)

S1 + S2 - L ~ N(0, 0.025^2 * 20)

P( -0.2 < S1 + S2 - L < 0.2 ) = {Use your GC}