Given data:
Mean: 66 in
Standard deviation: 1.5in
Find height is at the 35th percentile
Use the formula to find the z-score:
[tex]z=\frac{x-\mu}{\sigma}[/tex]z is the z-score corresponding to an area of 0.35 in the normal curve (35th percenlite)
μ is 66in
σ is 1.5in
Find the value of x corresponding to the given percentile:
1. Use a z-table to find the z score:
z=-0.39
2. Use the formula of z score and the given data to solve x:
[tex]\begin{gathered} -0.39=\frac{x-66}{1.5} \\ \\ 1.5(-0.39)=x-66 \\ \\ -0.585=x-66 \\ \\ -0.585+66=x \\ \\ x=65.415 \end{gathered}[/tex]Then, the 35th percentile is 64.4 inches
