Normal distributions are very commonly used for quality control in manufacturing. For example, a
Manufacturer of light bulbs would surely be interested in studying how long their bulbs last. In one
Case, the lifetime of one model of light bulb is normally distributed and has a mean X = 1,900 hours
And a standard deviation of s = 250 hours. What is the probability that a bulb will last between 1,650
And 1,900 hours?
A)0.5
B)0.341
C)0.841
D)50

Question

Normal distributions are very commonly used for quality control in manufacturing. For example, a
Manufacturer of light bulbs would surely be interested in studying how long their bulbs last. In one
Case, the lifetime of one model of light bulb is normally distributed and has a mean X = 1,900 hours
And a standard deviation of s = 250 hours. What is the probability that a bulb will last between 1,650
And 1,900 hours? 
A)0.5 
B)0.341 
C)0.841 
D)50

Quizplus · Accepted Answer

Since the lifetime of the bulb is normally distributed with a mean of 1,900 hours and a standard deviation of 250 hours, we can standardize the values for 1,650 hours and 1,900 hours using the formula z = (x - mean)/standard deviation.
z for 1,650 hours = (1,650 - 1,900)/250 = -1
z for 1,900 hours = (1,900 - 1,900)/250 = 0
Using a standard normal distribution table or calculator, we can find the area under the curve between z = -1 and z = 0, which is approximately 0.341. Therefore, the probability that a bulb will last between 1,650 and 1,900 hours is 0.341 or 34.1%. The correct answer is B. We need to find the probability that the bulb will last between 1,650 and 1,900 hours. We can use the standard normal distribution by standardizing the values first:

z1 = (1650-1900)/250 = -1
z2 = (1900-1900)/250 = 0

Using a standard normal table or a calculator, we can find the probability that a standard normal distribution is between -1 and 0 is 0.341. Therefore, the probability that the bulb will last between 1,650 and 1,900 hours is 0.341 or 34.1%. The correct answer is B.

Normal Distributions Are Very Commonly Used for Quality Control in Manufacturing