Question 266632: A brand of water softener salt comes in packages marked “net weight 40lb”. The company that packages the salt claims that the bags contain an average of 40lb of salt and that the standard deviation of the weight is 1.5lb. Assume that the weights are normally distributed.
a. Obtain the probability that the weight of one randomly selected bag of water-softener salt will be 39lb or less, if the company’s claim is true.
B. Determine the probability that the mean weight of 10 randomly selected bags of water-softener salt will be 39lb or less, if the company’s claim is true.
C. If you bought one bag of water-softener salt and it weighed 39lb,would you consider this evidence that the company’s claim is incorrect? Explain your answer
D. If you bought 10 bags of water-softener salt and their mean weight was 39lb, would you consider this evidence that the company’s claim is incorrect? Explain your answer
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A brand of water softener salt comes in packages marked “net weight 40lb”. The company that packages the salt claims that the bags contain an average of 40lb of salt and that the standard deviation of the weight is 1.5lb. Assume that the weights are normally distributed.
a. Obtain the probability that the weight of one randomly selected bag of water-softener salt will be 39lb or less, if the company’s claim is true.
P(x< 39) = normalcdf(-100,39,40,1.5)= 0.2525
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B. Determine the probability that the mean weight of 10 randomly selected bags of water-softener salt will be 39lb or less, if the company’s claim is true.
P(xbar< 39) = normalcdf(-100,39,40,1.5/sqrt(10)) = 0.0175...
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C. If you bought one bag of water-softener salt and it weighed 39lb,would you consider this evidence that the company’s claim is incorrect? Explain your answer
No, since 25% are expected to weight 39 or less.
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D. If you bought 10 bags of water-softener salt and their mean weight was 39lb, would you consider this evidence that the company’s claim is incorrect? Explain your answer
It would be strong evidece since less then 2% of such samples of 10 have a
mean less then 39.
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Cheers,
Stan H.
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