The lifetimes of lightbulbs of a particular type are normally distributed with a mean of 392 hours and a standard deviation of 9 hours. find the first quartile, q1.

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Mercer

Mathematics

28 May, 03:00

The lifetimes of lightbulbs of a particular type are normally distributed with a mean of 392 hours and a standard deviation of 9 hours. find the first quartile, q1.

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Kadin Dougherty · Answer 1

The 1st quartile q1 is also called the 25th percentile (the bottom 25% of a data set). In this case, if we choose 100 light bulbs, then the 1st quartile will be the 25 bulbs with shortest useful life.

To solve this problem, we would have to use the z statistic. Using the standard distribution tables for z, we locate for the value of z at P = 0.25:

z = - 0.674

Then to calculate for the 1st quartile, we use the formula:

Q1 = x + z * s

where x is the mean, and s is the standard deviation, therefore:

Q1 = 392 + ( - 0.674) (9)

Q1 = 385.934