The thickness of a washer (in \(\mathrm{mm}\) ) is a random variable with probability density function

a. What is the probability that the thickness is less than \(2.5 \mathrm{~m}\) ?

b. What is the probability that the thickness is between 2.5 and \(3.5 \mathrm{~m}\) ?

c. Find the mean thickness.

d. Find the standard deviation \(\sigma\) of the thicknesses.

e. Find the probability that the thickness is within \(\pm \sigma\) of the mean.

f. Find the cumulative distribution function of the thickness.

Transcribed Image Text:

f(x) = { -x(6-x) 0 52 2 < x < 4 otherwise