Elongation (in percent) of steel plates treated with aluminum are random with probability density function

a. What proportion of steel plates have elongations greater than 25%?

b. Find the mean elongation.

c. Find the variance of the elongations.

d. Find the standard deviation of the elongations.

e. Find the cumulative distribution function of the elongations.

f. A particular plate elongates 28%. What proportion of plates elongate more than this?

Solution

Step 1 of 5

Here given elongation of steel plates treated with aluminium are random

The given pdf is

=0, Otherwise

a) we need to find the proportion of steel plates have elongation greater than 25%

=1.8-1.25

=0.55

The proportion of steel plates have elongation greater than 25% is 0.55