You are studying a newly discovered species of rodent. Observations suggest that a rodent selected at random

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You are studying a newly discovered species of rodent. Observations suggest that a rodent selected at random with a tail of length described by a random variable X cm with probability density functionfx (x) = a sin(x) for x = [0,5]

where α is some constant.

a. Determine the value of α such that fX(x) is a valid probability density function.

b. Calculate the probability that a randomly selected adult rodent will have a tail of length between 4 and 4.5 cm.

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