Find the specified percentile, quartile, or decile.
-The annual precipitation for one city is normally distributed with a mean of 26 inches and a standard deviation of 4 inches. Find the 2nd decile.
A)22.64 inches
B)34.2 inches
C)29.36 inches
D)17.8 inches

Question

Find the specified percentile, quartile, or decile.
-The annual precipitation for one city is normally distributed with a mean of 26 inches and a standard deviation of 4 inches. Find the 2nd decile. 
A)22.64 inches
B)34.2 inches
C)29.36 inches
D)17.8 inches

Quizplus · Accepted Answer

The 2nd decile corresponds to the 20th percentile in a distribution. To find this value in a normal distribution, we use the Z-score formula. The Z-score for the 20th percentile is approximately -0.84. Using the formula $X = \mu + Z\sigma$, where $\mu$ is the mean, $\sigma$ is the standard deviation, and $Z$ is the Z-score, we calculate $X = 26 + (-0.84)(4) = 26 - 3.36 = 22.64$ inches.

Find the Specified Percentile, Quartile, or Decile