Question

A personal computer has the length of time between charges of the battery is normally distributed with a mean of 66 hours and a standard deviation of 20 hours. What is the probability when the length of time will be between 58 and 75 hours?

(a) 0.595

(b) 3.44

(c) 0.0443

(d) 1.98

This question was posed to me by my college professor while I was bunking the class.

This intriguing question comes from Probability Distribution topic in portion Discrete Probability of Discrete Mathematics

Answer 1

The correct answer is (c) 0.0443

The explanation is: Suppose x be the random variable that represents the length of time. It has a mean of 66 and a standard deviation of 20. Find the probability that x is between 70 and 90 or P(70 < x < 90). For x = 70, z = \(\frac{58 – 66}{20}\) = -4. For x = 75, z = \(\frac{75 – 66}{20}\) = 0.45. P(70 < x < 90) = P(-4 < z < 0.75) = [area to the left of z = 0.75] – [area to the left of z = -4] = 0.0443. The required  probability when the length of time between 58 and 75 hours is 0.0443.