Resistors labeled 100 Ω have true resistances that are between 80 Ω and 120 Ω. Let X be the mass of a randomly chosen resistor. The probability density function a. What proportion of resistors have resistances less than 90 Ω? b. Find the mean resistance.

See explanation for step by step explanations.

Explanation:

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

Step 2 of 4<

/p>

b) we have to find the mean resistance

Mean=

=

=

=106.67

The mean resistance is 106.67

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y