Question: The diameter of a rivet (in mm) is a random variable with probability density function. a. What is the probability that the diameter is less

The diameter of a rivet (in mm) is a random variable with probability density function.

(6(х — 12) (13 — х) 12 <x < 13 f(x) = otherwise


a. What is the probability that the diameter is less than 12.5 mm?

b. Find the mean diameter.

c. Find the standard deviation of the diameters.

d. Find the cumulative distribution function of the diameter.

e. The specification for the diameter is 12.3 to 12.7 mm. What is the probability that the specification is met?

(6( 12) (13 ) 12

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