Solution Found!
Resistors labeled 100 ? have true resistances that are
Chapter 2, Problem 13E(choose chapter or problem)
Resistors labeled \(100\ \Omega\) have true resistances that are between \(80\ \Omega\) and \(120\ \Omega\). Let be the mass of a randomly chosen resistor. The probability density function of
is given by
\(f(x)=\left\{\begin{array}{cl}
\frac{x-80}{800} & 80<x<120 \\
0 & \text { otherwise }
\end{array}\right.
\)
a. What proportion of resistors have resistances less than \(90\ \Omega\)?
b. Find the mean resistance.
c. Find the standard deviation of the resistances.
d. Find the cumulative distribution function of the resistances.
Equation Transcription:
Text Transcription:
100 ohms
80 ohms
120 ohms
f(x)={_0 otherwise ^{x-80}over{800} 80<x<120
90 ohms
Questions & Answers
QUESTION:
Resistors labeled \(100\ \Omega\) have true resistances that are between \(80\ \Omega\) and \(120\ \Omega\). Let be the mass of a randomly chosen resistor. The probability density function of
is given by
\(f(x)=\left\{\begin{array}{cl}
\frac{x-80}{800} & 80<x<120 \\
0 & \text { otherwise }
\end{array}\right.
\)
a. What proportion of resistors have resistances less than \(90\ \Omega\)?
b. Find the mean resistance.
c. Find the standard deviation of the resistances.
d. Find the cumulative distribution function of the resistances.
Equation Transcription:
Text Transcription:
100 ohms
80 ohms
120 ohms
f(x)={_0 otherwise ^{x-80}over{800} 80<x<120
90 ohms
ANSWER:
Solution
Step 1 of 4
Let X be the mass of a randomly selected resistor
The probability density function is given as
, 80<x<120
=0, otherwise
a) By using the given pdf we have to find the probability of the resistors having resistance less than 90
=
=
=0.0625
the probability of the resistors having resistance less than 90 is 0.0625