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natima [27]
3 years ago
15

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.
Physics
1 answer:
STatiana [176]3 years ago
5 0

Answer:

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

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   First, you need to determine the period of the function. The period will be the time interval between identical points on the sinusoidal function. For this problem, the tide is rising and at 5.15 at midnight for two consecutive days. So the period is 24 hours. Over that 24 hour period, we want the parameter passed to sine to range from 0 to 2*pi. So the scale factor for x will be 2*pi/24 = pi/12 which is approximately 0.261799388. The next thing to note is the magnitude of the wave. That will simply be the difference between the maximum and minimum values. So 10.2 ft - 0.1 ft = 10.1 ft. And since the value of sine ranges from -1 to 1, we need to divide that magnitude by 2, so 10.1 ft / 2 = 5.05 ft.

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   The final thing that might have been needed would have been a phase correction. With this problem, we don't need a phase correction since at X = 0 (midnight), the value of X*pi/12 = 0, and the sine of 0 is 0, so the value of the equation is 5.15 which matches the given value of 5.15. But if the problem had been slightly different and the height of the tide at midnight has been something like 7 feet, then we would have had to calculate a phase shift value for the function and add that constant to the parameter being passed into sine, making the function look like:
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   But we don't need it for this problem, so the answer is:
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   Note: The above solution assumes that angles are being measured in radians. If you're using degrees, then instead of multiplying x by 2*pi/24 = pi/12, you need to multiply by 360/24 = 15 instead, giving f(x) = 5.05*sin(x*15) + 5.15</span>
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