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a brand of water-softener salt comes in packages marked “net weight 40 lbs”. The company that...

a brand of water-softener salt comes in packages marked “net weight 40 lbs”. The company that packages the salt claims that the bags contain an average of 40 lbs of salt and that the standard deviation of the weight is 1.5lbs. Assume that the weights are normally dostributed.

Obtain the probability that a randomly selected bag of salt will be 39 lbs or less, if the company’s claim is true.
Math   Statistics-And-Probability   
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Answer #1

Mean, =40 lbs.

Standard deviation, =1.5 lbs.

X =39 lbs.

Standard Normal Variate, Z =(X - ​​​​​​)/​​​​​​ =(39 - 40)/1.5 = -0.6667

The probability that a randomly selected bag of salt will be 39 lbs or less =P(X 39) =P(Z - 0.67) =0.2525

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