Answer :
Answer:
the 13th percentile = 35.238
Step-by-step explanation:
We can find the 13th percentile by using the Z-score formula:
[tex]\boxed{Z=\frac{x-\mu}{\sigma} }[/tex]
where:
- [tex]Z=\text{Z-score}[/tex]
- [tex]x=\text{observed value}[/tex]
- [tex]\mu=\text{mean}[/tex]
- [tex]\sigma=\text{standard deviation}[/tex]
By using the normal distribution table, we can convert the 13th percentile (13%) into z-score:
[tex]P(X)=0.13[/tex]
[tex]Z(X)=-1.127[/tex]
Hence:
[tex]\begin{aligned}\\Z(X)&=\frac{x-\mu}{\sigma} \\\\-1.127&=\frac{x-42}{6} \\\\x-42&=6(-1.127)\\\\x&=-6.762+42\\\\x&=\bf 35.238\end{aligned}[/tex]
