Question

What are quartiles in this instance and how do I find them in this question?

QUESTION: The lengths of a grasshopper antennae are normally distributed with a mean length of 119.4 and a standard deviation of 34.7. Find the quartiles.

Answer 1

First quartile Q1

X ~ N ( µ = 119.4 , σ = 34.7 )
P ( X < x ) = 25% = 0.25
To find the value of x
Looking for the probability 0.25 in standard normal table to calculate critical value Z = -0.6745
Z = ( X - µ ) / σ
-0.6745 = ( X - 119.4 ) / 34.7
X = 95.99

Second quartile (Median)

X ~ N ( µ = 119.4 , σ = 34.7 )
P ( X < x ) = 50% = 0.5
To find the value of x
Looking for the probability 0.5 in standard normal table to calculate critical value Z = 0
Z = ( X - µ ) / σ
0 = ( X - 119.4 ) / 34.7
X = 119.4

Third quartile Q3

X ~ N ( µ = 119.4 , σ = 34.7 )
P ( X < x ) = 75% = 0.75
To find the value of x
Looking for the probability 0.75 in standard normal table to calculate critical value Z = 0.6745
Z = ( X - µ ) / σ
0.6745 = ( X - 119.4 ) / 34.7
X = 142.805