Based on data from a dart-throwing experiment, the article “Shooting Stars” in C

Question

Based on data from a dart-throwing experiment, the article “Shooting Stars” in Chance proposed that the horizontal and vertical errors from aiming at a point target should be independent of one another, each with a normal distribution having mean = 0 and = 20mm. (It can then be shown that the pdf of the squared distance between the point target and the landing point T, divided by the variance, follows a Chi-Squared probability density function with = 2 degrees of freedom). What is the probability that a dart will land within 48.957mm of the target?

Explanation / Answer

WE HAVE BEEN GIVEN MEAN = 0

STANDARD DEVIATION = 20

Z = (X-MEAN)/STANDARD DEVIATION

HERE X = 48.957

NOW WE NEED TO FIND P(X<48.957) =

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