Question

Elongation (in percent) of steel plates treated with aluminum are random with probability density function. What proportion of steel plates have elongations greater than 25%

Answer 1

According to the probability density function given, it is found that 0.2813 = 28.13% of steel plates have elongations greater than 25%.

What is the probability density function for the elongation of steel plates?

Researching the problem on the internet, it is found that the elongation of steel plates treated with aluminum are random with probability density function given as follows:

$p(x) = \frac{x}{400}, 15 \leq x \leq 30$

The proportion of steel plates have elongations greater than 25% is given by:

$p = \int_{25}^{30} p(x) dx$

$p = \int_{25}^{30} \frac{x}{400} dx$

$p = \frac{x^2}{800}|_{x = 25}^{x = 30}$

Applying the Fundamental Theorem of Calculus:

$p = \frac{30^2}{800} - \frac{25^2}{800}$

$p = 0.2813$

0.2813 = 28.13% of steel plates have elongations greater than 25%.

You can learn more about probability density functions at https://brainly.com/question/14683948