Answer:
Okay, let's solve this problem in steps:
The lifespan of Bright Inc. light bulbs follows a normal distribution with a mean (μ) of 300 days and standard deviation (σ) of 40 days.
To find the 20th percentile, we calculate:
20th percentile = μ - σ * 0.842
= 300 - 40 * 0.842
= 255 days
20% of light bulbs survive less than the 20th percentile.
So 20% of Bright Inc. light bulbs survive less than 255 days.
In summary, 20% of light bulbs produced by Bright Inc. survive less than 255 days.
Let's break this down further step-by-step:
A normal distribution is symmetrical and bell-shaped. The mean (μ=300 days) is the center of the distribution. The standard deviation (σ=40 days) describes the spread/variance of the distribution.
To find percentiles other than the mean, we use the equation:
Percentile = μ - σ * z-score
Here, the 20th percentile z-score is 0.842.
So 20th percentile = 300 - 40 * 0.842 = 255
Since 20% of the data lies below the 20th percentile, 20% of the light bulbs will have lifespans less than 255 days.
If the mean was higher (say 350 days), the 20th percentile and lifespan less than would also be higher (around 300-310 days).
If the standard deviation was higher (say 60 days), the 20th percentile range would be wider ( 245 to 265 days) indicating more variability.
Explanation: