A batch of small caliber ammunition is accepted as satisfactory if none of a sample of
five shots falls more than 2 meters from the center of the target at a given range. If X, the
distance from the center of the target to a given impact point, actually has the probability
density function
f(x) = 2kx exp(−x^2), 0 < x < 3,
where k is a number which makes it probability density function, what is the value of k
and what is the probability that the batch will be accepted?
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