A new extended-life light bulb has an average life of 750 hours, with a standard deviation of 50 hours. If the life of these light bulbs approximates a normal distribution, about what percent of the distribution will be between 600 hours and 900 hours?
A) 95%
B) 68%
C) 34%
D) 99.47%

Question

Quizplus · Accepted Answer

To solve this problem, we need to use z-scores and the standard normal distribution. We can first standardize the values of 600 and 900 using the formula:

z = (x - μ) / σ

where μ is the mean and σ is the standard deviation. Substituting the values:

z1= (600 - 750) / 50 = -3.00
z2 = (900 - 750) / 50 = 3.00

We can then use a standard normal distribution table or a calculator to find the area under the curve between these z-scores.

The area between -3.00 and 3.00 is about 0.9947 or 99.47%, which means that about 99.47% of the distribution will be between 600 hours and 900 hours. Therefore, the best choice is D.

A New Extended-Life Light Bulb Has an Average Life of 750