Birth weights are normally distributed with a mean of 3419 g and a standard deviation of 494 g. if a hospital plans to set up special attention to the lightest 2% of babies, what weight is used for the cut-off separating the lightest 2% from the others?

Let X represent a random variable representing the birth weights of babies, and let x be the required cut-off, then
P(X < x) = 0.02
P(z < (x - 3419)/494) = 0.02
1 - P(z < (3419 - x)/494) = 0.02
P(z < (3419 - x)/494) = 1 - 0.02 = 0.98
(3419 - x)/469 = 2.04
3419 - x = 956.76
x = 3419 - 956.76 = 2462.24

Therefore, the weight to be used as cut-off is 2462.24 g

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