The probability density function of the length of a metal rod is f(x) = 2.0 for 2.3 < x < 2.8 meters. if the specifications for this process are from 2.25 to 2.75 meters, what proportion of the bars fail to meet the specifications? assume that the probability density function is f(x) = 2.0 for an interval of length 0.5 meters. over what value should the density be centered to achieve the greatest proportion of bars within specifications?

answer is 33

step-by-step explanation:

answer: solve 5\cdot 2^x=2405⋅2  

x

=2405, dot, 2, start superscript, x, end superscript, equals, 240.

solution

to solve for xxx, we must first isolate the exponential part. to do this, divide both sides by 555 as shown below. we do not multiply the 555 and the 222 as this goes against the order of operations!

\begin{aligned} 5\cdot 2^x& =240 2^x& =48 \\ \end{aligned}  

5⋅2  

x

2  

x

​    

=240

=48

​

step-by-step explanation: