Find the specified percentile, quartile, or decile.
-The amount of Jen's monthly phone bill is normally distributed with a mean of $54 and a standard deviation of $8. Find the first quartile, $\mathrm { Q } _ { 1 } .$
A)$56
B)$59.36
C)$50
D)$48.64

Question

Find the specified percentile, quartile, or decile.
-The amount of Jen's monthly phone bill is normally distributed with a mean of $54 and a standard deviation of $8. Find the first quartile, $\mathrm { Q } _ { 1 } .$ 
A)$56
B)$59.36
C)$50
D)$48.64

Quizplus · Accepted Answer

The first quartile, $Q_1$, corresponds to the 25th percentile in a distribution. For a normal distribution, we can use the Z-score formula to find the value at a specific percentile. The Z-score for the 25th percentile is approximately -0.674 (from Z-tables or standard normal distribution tables). Using the formula $X = \mu + Z\sigma$, where $\mu$ is the mean, $\sigma$ is the standard deviation, and $Z$ is the Z-score, we can calculate $X$ as follows: $X = 54 + (-0.674)(8) = 54 - 5.392 = 48.608$. Rounding to two decimal places, the closest answer is $48.64.

Find the Specified Percentile, Quartile, or Decile Q1.\mathrm { Q } _ { 1 } .Q1​.

Find the Specified Percentile, Quartile, or Decile $\mathrm { Q } _ { 1 } .$