The diameter of rod produced in a lathe X during mass produc

The diameter of rod produced in a lathe (X) during mass production of nominal dia 20 mm, is known to follow the following distribution: fX(x) = o when x<20 mm = 15 exp(-15*(x-20)) when x>=20 mm Determine the following: 2.1 probability distribution function of diameter of rod (5 points) (1 Point) 2.2 if rods with diameter larger than 20.2 mm are not acceptable, determine the proportion of rods that are accepted and rejected (10 points) (1 Points) 2.3 Find mean and standard deviation of X (5 points) (2 Points)

Solution

The diameter of rod produced in a lathe (X) during mass production of nominal dia 20 mm, is known to follow the following distribution: fX(x) = o when x<20 mm = 15 exp(-15*(x-20)) when x>=20 mm Determine the following: 2.1 probability distribution function of diameter of rod (5 points) (1 Point) 2.2 if rods with diameter larger than 20.2 mm are not acceptable, determine the proportion of rods that are accepted and rejected (10 points) (1 Points) 2.3 Find mean and standard deviation of X (5 points) (2 Points)