Question

The life of a manufacturer's compact fluorescent light bulbs is normal, with mean 12,000 hours and standard deviation 2,000 hours. Seth wants to find the probability that a light bulb he purchased from this manufacturer will last no more than 14,500 hours. How many standard deviations above the mean is 14,500 hours? 1. 25 1. 5 2. 5.

Answer 1

Z value is a numerical  measurement that describe a value relationship to the mean of a group of values. The standard deviations is 1.25 above the mean is 14,500 hours.

Given information-

The mean for the bulb is 12,000 hours.

The standard deviation for the bulb is 2000 hours.

Sample value is 14500.

To find out the how many standard deviation is 14500 mean away from the mean the z value of the mean should be calculated.

Z value

Z value is a numerical  measurement that describe a value relationship to the mean of a group of values. Z value is the ratio of the difference of the sample value $x$ and mean $\mu$ to the standard deviation. Thus the z value for the given mean $\sigma$ is,

$z=\dfrac{x-\mu}{\sigma}$

$z=\dfrac{14500-1200}{2000}$

$z=1.25$

Thus the standard deviations is 1.25 above the mean is 14,500 hours.

Learn more about the z value here;

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