class of 30 of these pupils is used as sample. what is the probability that the class mean is greater than 46 inches
Let "X=" the class mean: "X\\sim N(\\mu, \\sigma^2\/n)"
Then "Z=\\dfrac{X-\\mu}{\\sigma\/\\sqrt{n}}\\sim N(0, 1)"
Given "\\mu=45, \\sigma=2, n=30"
"=1-P(Z\\leq\\dfrac{46-45}{2\/\\sqrt{30}})\\approx1-P(Z\\leq2.7386128)"
"\\approx1-0.996915\\approx0.003085"
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