The amount of sugar (X) contained in 2-kg packets is actually normally distributed with a mean...

 

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The amount of sugar (X) contained in 2-kg packets is actually normally distributed with a mean of u = 2.03 kg and a standard deviation of o = 0.014 kg. (a) What proportion of sugar packets are underweight? (b) If an alternative package-filling machine is used for which the weights of the packets are normally distributed with a mean of u = 2.05 kg and a standard deviation of o = 0.016 kg, does this result in an increase or a decrease in the proportion of underweight packets? (c) What is the probability that the amount of sugar of a randomly selected bearing is between 1 and 2 SDs from its mean value? (d) What is the value of c for which there is a 95% probability that a packet weight is within the interval [2.03 c, 2.03 + c]? (e) What is the value of c for which there is a 95% probability that a packet weight is within the interval [2.5 – c, 2.5 + c]? The amount of sugar (X) contained in 2-kg packets is actually normally distributed with a mean of u = 2.03 kg and a standard deviation of o = 0.014 kg. (a) What proportion of sugar packets are underweight? (b) If an alternative package-filling machine is used for which the weights of the packets are normally distributed with a mean of u = 2.05 kg and a standard deviation of o = 0.016 kg, does this result in an increase or a decrease in the proportion of underweight packets? (c) What is the probability that the amount of sugar of a randomly selected bearing is between 1 and 2 SDs from its mean value? (d) What is the value of c for which there is a 95% probability that a packet weight is within the interval [2.03 c, 2.03 + c]? (e) What is the value of c for which there is a 95% probability that a packet weight is within the interval [2.5 – c, 2.5 + c]?