Normal Probability Key Samples

# Normal Probability Key Samples - Normal Distribution...

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Unformatted text preview: Normal Distribution Calculations Activity Name ____________________ Section ____ 1. For several years student survey teams have measured the terrain around campus. Each team must measure the increase in elevation from the US flagpole to the top of a nearby, small hill. The measurements of teams that are obviously in error are omitted. From many past good team measurements we know that the rise in elevation is 4.537 meters and that the standard deviation for good measurements is 0.113 meters. The teams make different measurements, because of random measurement error. This error is distributed normally. This year survey teams will measure the rise in elevation, too. X ~ NORM(4.537, 0.113) a. What is the probability that a good survey team’s measurement will be less than 4.493 meters? P(X < 4.493) = P(Z < ζ ), find ζ : ζ = ( χ – μ )/ σ = (4.493-4.537) / 0.113 ζ = -0.38939, so use -0.39, P(Z<-0.39) = 0.3483 b. What is the probability that a good survey team’s measurement will be greater than 4.591meters? P(X > 4.591) = 1 - P(X< 4.591) = 1 - P(Z < ζ ), find ζ : ζ = ( χ – μ )/ σ = (4.591-4.537) / 0.113 ζ = 0.477876, so use 0.48, 1 - P(Z<0.48) = 1 - 0.6844 = 0.3156 c. What is the probability that a good survey team’s measurement will be between 4.385 and 4.601 meters? P(4.385 < X 4.601) = P(X < 4.601) - P(X< 4.385) = P(Z < ζ hi ) - P(Z < ζ lo ), Find ζ hi : ζ hi = ( χ – μ )/ σ = (4.601-4.537) / 0.113 = 0.56637; use 0.57= (4....
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Normal Probability Key Samples - Normal Distribution...

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