If the diameter X of axles has the density fx k if 24975 les

If the diameter X of axles has the density f(x)= k if 249.75 lessthanorequalto x lessthanorequalto 250.25 and 0 otherwise, how many defectives will a lot of 600 axles approximately contain if defectives are slimmer than 249.95 or thicker than 250.15?

Solution

Assume that the diameter of the 600 axles are in between the limits 249.75 to 250.25. and are evenly distributed in between the range.

lets divide the range into 5 groups. according to the assumption (600/5)=120 number of axles will fall in 1 group.

120 axles has diameter in between 249.75- 249.85

120axles has diameter in between 249.85- 249.95

120 axles has diameter in between 249.95- 250.05

120 axles has diameter in between 250.05- 250.15

120 axles has diameter in between 250.15- 250.25

so axles that fall in between the first 2 groups and the last group are defective.

so approximately (120+120+120)=360 are defective in alot of 600 axles.