Solve the problem. The lifetime of a new brand of light bulb can be described by a Normal model with a mean of 2000 hours and a standard deviation of 250 hours. Find the percentage of light bulbs that will last more than 2600 hours.
A.) 100%
B.) 5%
C.) 99.18%
D.) 0.82%
E.) Cannot be determined
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to that Z score.
To find the percentage of light bulbs that will last more than 2600 hours, we can use the properties of the normal distribution.
First, we need to calculate the z-score for 2600 hours using the formula:
z = (x - μ) / σ
Where:
x = 2600 hours (the value we want to find the probability for)
μ = mean = 2000 hours
σ = standard deviation = 250 hours
z = (2600 - 2000) / 250
z = 600 / 250
z = 2.4
Next, we can use a standard normal distribution table or calculator to find the percentage of light bulbs that last more than 2600 hours, which corresponds to the area under the curve to the right of the z-score.
Looking up the z-score of 2.4 in the standard normal distribution table, we find the corresponding area to be approximately 0.9918.
Since we want to find the percentage *more* than 2600 hours, we need to subtract the area corresponding to 2.4 from 1.
1 - 0.9918 = 0.0082
Multiplying this by 100 to express it as a percentage, we find that the percentage of light bulbs that will last more than 2600 hours is approximately 0.82%.
Therefore, the correct answer is option D.) 0.82%.