Tom is testing the accuracy of resistors that have a labeled resistance of 15 (ohms).?

Question

He finds that the distribution of resistances is approximately normal with a mean resistance 15.08 and a standard deviation of 1.52 .

What is the probability of each of the following?
a. A resistor selected randomly has a resistance less than or equal to 14 ohms

b. A resistor selected randomly has a resistance between 14.08  ohms and 16.08 ohms

c A resistor selected has a resistance of exactly 15.5 ohms

jake · Answer

hello thanks for the answer how do you show the answer for c A resistor selected has a resistance of exactly 15.5 ohms being 0?

The Gnostic · Answer

(a)
14 ohms is 1.08 ohms less than the mean, which is 0.7105… standard deviations below the mean.  P(Z < .71) = 0.2389

(b)
14.08 is .66 sd below, and 16.08 is .66 sd above.  P(Z < .66) - P(Z < -.66) = 0.4908

(c)
zero

//// in answer to your follow-up question ////
The probability of a chosen resistor having an EXACT value is 1/(the total number of possible resistances).  Since the resistances are continuous, this "total number" tends toward infinity, making the fraction equal zero.

Trending News

Tom is testing the accuracy of resistors that have a labeled resistance of 15 (ohms).?

2 Answers