[See Solution] (10) Global Positioning Systems (GPS), using satellites, can determine the latitude, longitude, and altitude of a hand-held GPS sensor on


Question: (10) Global Positioning Systems (GPS), using satellites, can determine the latitude, longitude, and altitude of a hand-held GPS sensor on the ground with great accuracy. Suppose that the errors X, Y, and Z (in meters) in these three coordinates are independent, normally distributed random variables with mean 0 and standard deviation ½ meter. What is the probability that the overall GPS position in three-dimensional space is accurate to within 1 meter ?

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