SOLUTION: A brain of water softener salt comes in package marked net weight 40 lb. The company that packages it claims that the bag contains an average of 40lb of salt and the standard devia

Question 298234: A brain of water softener salt comes in package marked net weight 40 lb. The company that packages it claims that the bag contains an average of 40lb of salt and 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 39 lb 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 39 lb or les if the company's claim is true.
c. I you bought one bag of water-softener salt and it weighed 39 lb, 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 39 lb, 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 package marked net weight 40 lb. The company that packages it claims that the bag contains an average of 40lb of salt and 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 39 lb or less if the company's claim is true.
Find the z-value of 39 using u = 40 and sigma = 1.5:
z(39) = (39-40)/1.5 = -1/1.5 = -2/3
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Then find the probability z< -2/3
P(z, -2/3) = normalcdf(-100,-2/3) = 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 39 lb or less if the company's claim is true.
Find the t-value of 39 using u = 40 and s = 1.5/sqrt(10):
t(39) = (39-40)/[1.5/srt(10)] = -2.1082
Then find the probaility t< -2.1082 when df = 9
P(t< -2.1082 with df = 9) = tcdf(-100,-2.1082,9) = 0.0321
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c. If you bought one bag of water-softener salt and it weighed 39 lb, would you consider this evidence that the company's claim is incorrect? Explain your answer.
Determine the z-value of 39 as a number of standard deviations away from
the mean using sigma = 1.5.
z(39) = -2/3
Make your decision.
The weight of the bag is 2/3 of a standard devation below the mean weight.
That is not unusual; the company's claim might still be correct.
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d. If you bought 10 bags of water-softener salt and their mean weight was 39 lb, would you consider this evidence that the company's claim is incorrect? Explain your answer.
t(39) is more than 2 standard deviations below the mean. That is significant.
The company's claim may be incorrect.
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Cheers,
Stan H.
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