Compact fluorescent bulbs are more energy-efficient than incandescent bulbs, but they take longer to reach full brightness. The time it takes for a compact fluorescent bulb to reach full brightness is normally distributed with mean 29.9 seconds and standard deviation 4.9 seconds. Find and interpret the z-score for x=26.1.
A) z=0.71: the time to reach full brightness is 0.71 standard deviations above the mean.
B) z=0.71: the time to reach full brightness is 0.71 standard deviations below the mean.
C) z=-0.78 : the time to reach full brightness is 0.78 standard deviations below the mean.
D) z=-0.78: the time to reach full brightness is 0.78 standard deviations above the mean.

Question

Quizplus · Accepted Answer

To find the z-score, we use the formula:

z = (x - μ) / σ

where x is the value we want to find the z-score for, μ is the mean, and σ is the standard deviation.

Plugging in the given values, we get:

z = (26.1 - 29.9) / 4.9

z = -0.78

This means that the time it takes for the bulb to reach full brightness at 26.1 seconds is 0.78 standard deviations below the mean. Therefore, the best choice is C.

Compact Fluorescent Bulbs Are More Energy-Efficient Than Incandescent Bulbs, but They