Note: You are supposed to use Markov and chebichef inequalities. Boxes of a cert

Question

Note: You are supposed to use Markov and chebichef inequalities.

Boxes of a certain kind of cookie have an average weight of 12 ounces. With what probability can we assert that the weight of a randomly chosen box will be less than 15 ounces?

With reference to problem 2, suppose we also know that the standard deviation of box weight is 1.5 ounces. With what probability can we assert that the weight of a randomly chosen box will be between 10 and 14 ounces? 2. Boxes of a certain kind of cookie have an average weight of 12 ounces. With what probability can we assert that the weight of a randomly chosen box will be less than 15 ounces?

Explanation / Answer

1) from MArkov  inequalities P(X>t )<= E(X)/t

therefore probability that the weight of a randomly chosen box will be less than 15 ounces

=P(X<15) =1-P(X>15 )>=1-E(X)/15 >= 1-12/15 >=1/5

therefore we can assert that with at least probability of 1/5

2) here 10and 14 are (k=2/1.5=4/3 ) std deviation away from mean.,

thefore from Chebychef's inequality probability  that the weight of a randomly chosen box will be between 10 and 14 ounces =1-1/k2 =1-1/(4/3)2 =1-9/16=7/16

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