Suppose that weights of bags of potato chips coming from a factory follow a normal distribution with mean 12.8 ounces and standard deviation .6 ounces. If the manufacturer wants to keep the mean at 12.8 ounces but adjust the standard deviation so that only 1% of the bags weigh less than 12 ounces, how small does he/she need to make that standard deviation?
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What is needed is
P(X > 12) = 0.99
P(Z > (12-12.8)/Sd) = 0.99
P(Z > -0.8/Sd) = 0.99
But, P(Z > -2.33) = 0.99 from table
Therefore, -0.8/Sd = -2.33.
Sd = 0.3433. This should be the Sd.
P(X > 12) = 0.99
P(Z > (12-12.8)/Sd) = 0.99
P(Z > -0.8/Sd) = 0.99
But, P(Z > -2.33) = 0.99 from table
Therefore, -0.8/Sd = -2.33.
Sd = 0.3433. This should be the Sd.