Answer to Question #110813 in Statistics and Probability for Festus Shatilwe

Question

. The average weight of bags of maize meal packed at a particular farm is assumed to be normally distributed with a mean of 20 kg and a standard deviation of 3.0 kg. Determine the probability that a bag weighs between 19.5 kg and 22.0 kg?

Answer 1

$Given \; that, μ=20, σ=3, then,\\ P(19.5<x<22) = P(\frac{19.5-20}{3}< Z <\frac{22-20}{3})\\ =P(-0.17<Z<0.67)\\= P(0<Z<0.17)+ P(0<Z<0.67)\\ =0.0675+0.2486=0.3161\\$