Find the specified percentile, quartile, or decile.
-Suppose that replacement times for washing machines are normally distributed with a mean of 11 years and a standard deviation of 1 years. Find the 82nd percentile.
A)10.1 years
B)11.2 years
C)11.1 years
D)11.9 years

Question

Find the specified percentile, quartile, or decile.
-Suppose that replacement times for washing machines are normally distributed with a mean of 11 years and a standard deviation of 1 years. Find the 82nd percentile. 
A)10.1 years
B)11.2 years
C)11.1 years
D)11.9 years

Quizplus · Accepted Answer

To find the 82nd percentile of a normally distributed dataset, we use the Z-score formula and the standard normal distribution table. The Z-score corresponding to the 82nd percentile is approximately 0.92. Using the formula $X = \mu + Z\sigma$, where $\mu = 11$ years (mean) and $\sigma = 1$ year (standard deviation), we calculate $X = 11 + 0.92(1) = 11.92$ years, which rounds to 11.9 years, making option D correct.

Find the Specified Percentile, Quartile, or Decile