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A tea bag manufacturer needs to place 2 g of tea in each bag. If the machinery places a mean of 2.6 g of tea in each bag with a standard deviation of 0.3 g, what is the probability that a randomly chosen bag will have between 2 and 2.8 g of tea, assuming that the amounts of tea per bag are normally distributed? 17. WI
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Step 1: Sketch the curve. The probability that 2< X2.8 is equal to the blue area under the curve. 1.2 1.0 0.6 0.4 0.2 0.2 1.6 18 20 2.2 2.4 26 28 32 343.6 Step 2: Since μ 2.6 and σ 0.3 we have. 2-2.6 X-μ 2.8 2.6 < Since Z2 26 0.3 2.8 2.6 0.3 -2 and 0.67 we have: P(2< X28) P-2< Z<0.67) Step 3: Use the standard normal table to conclude that: P ( -2 < Z < 0.67 ) 0.7258

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