Find the specified percentile, quartile, or decile.
-The lifetimes of lightbulbs of a particular type are normally distributed with a mean of 263 hours and a standard deviation of 8 hours. Find the first quartile, Q1 .
A)257.64
B)268.36
C)265
D)261

Question

Find the specified percentile, quartile, or decile.
-The lifetimes of lightbulbs of a particular type are normally distributed with a mean of 263 hours and a standard deviation of 8 hours. Find the first quartile, Q1 . 
A)257.64
B)268.36
C)265
D)261

Quizplus · Accepted Answer

The first quartile, Q1, corresponds to the 25th percentile in a distribution. For a normal distribution, percentiles can be found using the Z-score formula: Z = (X - μ) / σ, where X is the value in the distribution, μ is the mean, and σ is the standard deviation. The Z-score for the 25th percentile is approximately -0.674 (from Z-tables or normal distribution calculators). Solving for X gives X = Zσ + μ = (-0.674)(8) + 263 = 257.64.

Find the Specified Percentile, Quartile, or Decile