A manufacturing plant uses a specific bulk product. The amount of product used in one day can be modeled by an exponenti

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A manufacturing plant uses a specific bulk product. The amount
of product used in one day can be modeled by an exponential
distribution with β=4 (measurements in tons).

a. How much of the bulk product should be stocked so that the
plant’s chance of running out of the product is only 0.05?
b. What is the probability that Y, the amount of product produced
in one day, will take a value that falls within 2 standard
deviations of its mean? Please do not use Chebyshev’s theorem.