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
