Asked Jan 22, 2020

Express the quartiles, Q1, Q2, and Q3, of a normally distributed variable in terms of its mean, µ, and standard deviation, σ.


Expert Answer

Step 1

First Quartile (Q1)

From the given information the first quartile is represented by 25th percentile and it separates the bottom 25% of the data from the top 75%.

Here, the 25th percentile represents the area of 0.25 to the left of z.

Use the standard normal table to find the area,


  • Locate the area of 0.25 in the standard normal table.
  • Move let until the first column and notes the value as –0.6.
  • Move upward until the top row is reached and note the value as 0.07.

The z-score is –0.67.

The first quartile calculated by

Statistics homework question answer, step 1, image 1
Step 2

Second Quartile (Q2)

The second quartile is represented by 50th percentile and it separates the bottom 50% of the data from the top 50%.

Here, the 50th percentile represents the area of 0.50 to the left of z.

Use the standard normal table to find the area,


  • Locate the area of 0.50 in the st...
Statistics homework question answer, step 2, image 1

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