a) The weights of bags filled by a machine are normally distributed with a stand

Question

a) The weights of bags filled by a machine are normally distributed with a standard deviation of 0.5 kg and a mean that can be set by the operator. At what level should the mean weight be set if it required that only 2.5% of the bags weigh less than 10 kg?

b) Assume that the gestational age (in days) in high risk pregnacies is approximately normally distributed with a standard deviation of 4 days. If we sample 49 high risk pregnacies, what is the probablity that the sample mean is within 1 day of the true mean gestational age ()?

Explanation / Answer

a)

standard deviation = 0.5 kg

let the mean be m

z value for p =0.025 is -1.96

z value for 10 is (10-m)/0.5

so (10-m)/0.5 = -1.96 => 10-m = 0.5*(-1.96) = -0.98

m = 10+0.98 = 10.98

mean weight should be set to 10.98kg  if it required that only 2.5% of the bags weigh less than 10 kg

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