SOLUTION: A market gardener in Tonga sells cabbages to a supermarket. She claims that the weights of the cabbages have a normal distribution with a mean weight of 1200 grams and a standard d

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Question 1116239: A market gardener in Tonga sells cabbages to a supermarket. She claims that the weights of the cabbages have a normal distribution with a mean weight of 1200 grams and a standard deviation of 50 grams.
(i) A cabbage is chosen at random, calculate the probability that its recorded weight is less than 1190 grams.
(ii) A consumer officer for the supermarket checks the gardener’s claim by weighing 40 of the cabbages. If the market gardener’s claim is true, calculate the probability that the 40 cabbages have a mean weight of less than 1190 grams.
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
z=(x-mean)/sd
=(1190-1200)/50
=-.2
Probability z< -.2 is 0.4207
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for 40 cabbages the denominator is sd/sqrt(n)
z=(-10)/50/sqrt(40)
=-10*sqrt(40)/50=-1.26
Probability z < -1.26 is 0.1038