A tree of this type grows in my backyard, and it stands 72.9 feet tall. Find the probability that the height of a randomly selected tree is as tall as mine or shorter.
My neighbor also has a tree of this type growing in her backyard, but hers stands 87.8 feet tall. Find the probability that the full height of a randomly selected tree is at least as tall as hers.
Answer :
Given :
The population mean $(μ)=67.2$
The population standard deviation $(σ)=7.1$
Solution :
A) The Probability Tree Is As Tall As or Shorter Than 72.9 Feet :
$$\therefore P(x < 72.9) = P\left(\frac{x – \mu}{\sigma} < \frac{72.9 – 67.2}{7.1}\right)$$ $$= P(z < 0.8)$$ $$= 0.7881$$
B) The Probability Tree Is At Least As Tall As 87.8 Feet :.
$$\therefore P(x > 87.8) = P\left(\frac{x – \mu}{\sigma} > \frac{87.8 – 67.2}{7.1}\right)$$ $$= P(z > 2.9)$$ $$= 0.0019$$
