The first quartile is the number in between the lowest number of a data set and the median. To find it, I would use a Z table as shown below
The z score that corresponds to 0.25 is -0.67 on the table above.
Using the equation of z-score below
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ \text{Where}\mu=\operatorname{mean},\sigma=s\tan dard\text{ deviation} \end{gathered}[/tex]Where x is the value we're looking for and σ and μ are the standard deviations and the mean given in the problem.
Given that the mean is 100.4 and the standard deviation is 19.7, make x the subject of the z-score formula and substitute for the mean and standard deviation as shown below
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ x-\mu=z\times\sigma \\ x=z\times\sigma+\mu \\ z=-0.67,\mu=100.4,\sigma=19.7 \end{gathered}[/tex][tex]\begin{gathered} x=-0.67\times19.7+100.4 \\ x=-13.199+100.4 \\ x=87.201 \end{gathered}[/tex]Hence, the first quartile is 87.201
