Answer:
Male giraffe: [tex]-0.67[/tex]
Female giraffe: [tex]-0.47[/tex]
Step-by-step explanation:
We have been given that the heights of female giraffes are approximately normal with mean 15.5 feet and standard deviation 3.6 feet. Male giraffes have mean height 16.8 feet with standard deviation 4.5 feet. We are asked to find the z-scores for a female giraffe 13.8 feet tall and a male 13.8 feet tall.
We will use z-score formula to solve our given problem.
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Let us find the z-score for male giraffes.
[tex]z=\frac{13.8-16.8}{4.5}[/tex]
[tex]z=\frac{-3}{4.5}[/tex]
[tex]z=-0.66666\approx -0.67[/tex]
Therefore, the z-score for a male giraffe that is 13.8 feet tall would be [tex]-0.67[/tex].
Let us find the z-score for female giraffes.
[tex]z=\frac{13.8-15.5}{3.6}[/tex]
[tex]z=\frac{-1.7}{3.6}[/tex]
[tex]z=-0.4722\approx -0.47[/tex]
Therefore, the z-score for a female giraffe that is 13.8 feet tall would be [tex]-0.47[/tex].
