Question

What is the probability that a resistor from a population with a normal distribution, a mean resistance of 22.00 kohm, and a standard deviation of 0.15 kohm, will have a resistance greater than 21.75kohm and less than or equal to 21.90kohm ?

Answer 1

The probability that a resistor will have a resistance greater than 21.75 kohm and less than or equal to 21.90 kohm is the difference between the cumulative probability corresponding to the z-score of -0.67 and the cumulative probability corresponding to the z-score of -1.67.

Step-by-step explanation:

To find the probability that a resistor from a population with a normal distribution will have a resistance greater than 21.75 kohm and less than or equal to 21.90 kohm, we need to standardize these resistance values using z-scores. The z-score formula is given by (x - μ) / σ, where x is the resistance value, μ is the mean resistance, and σ is the standard deviation. Let's calculate the z-score for 21.75 kohm:

z = (21.75 - 22.00) / 0.15 = -1.67

Next, let's calculate the z-score for 21.90 kohm:

z = (21.90 - 22.00) / 0.15 = -0.67

Now, we can use the standard normal distribution table or a calculator to find the probability associated with these z-scores. The probability that a resistor will have a resistance greater than 21.75 kohm and less than or equal to 21.90 kohm is the difference between the cumulative probability corresponding to the z-score of -0.67 and the cumulative probability corresponding to the z-score of -1.67.