Answer to Question #169295 in Statistics and Probability for Piyush

Question #169295

class of 30 of these pupils is used as sample. what is the probability that the class mean is greater than 46 inches


1
Expert's answer
2021-03-08T19:14:05-0500

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"


"P(X>46)=1-P(X\\leq 46)"

"=1-P(Z\\leq\\dfrac{46-45}{2\/\\sqrt{30}})\\approx1-P(Z\\leq2.7386128)"

"\\approx1-0.996915\\approx0.003085"

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