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 = 1,800 hours
And a standard deviation of s = 250 hours. What percentage of bulbs would you expect to last longer
Than 2,550 hours?
A)2.3%
B)0.1%
C)50%
D)99.9%

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 = 1,800 hours
And a standard deviation of s = 250 hours. What percentage of bulbs would you expect to last longer
Than 2,550 hours? 
A)2.3% 
B)0.1% 
C)50% 
D)99.9%

Quizplus · Accepted Answer

We need to find the percentage of bulbs that last longer than 2,550 hours.

We can standardize the variable using the formula:

z = (x - μ) / σ

where: 
x = 2,550 hours 
μ = 1,800 hours 
σ = 250 hours

z = (2,550 - 1,800) / 250 = 3

Using a standard normal distribution table or calculator, we can find that the percentage of values that fall above z = 3 is approximately 0.1%. Therefore, we can expect that only 0.1% of bulbs will last longer than 2,550 hours.

Normal Distributions Are Very Commonly Used for Quality Control in Manufacturing