Let represent the full height of a certain species of tree. Assume that has a normal probability distribution with a mean of 99.8 ft and a standard deviation of 5.4 ft.

Question

A tree of this type grows in my backyard, and it stands 100.9 feet tall. Find the probability that the height of a randomly selected tree is as tall as mine or shorter.

 = Incorrect

My neighbor also has a tree of this type growing in her backyard, but hers stands 104.1 feet tall. Find the probability that the full height of a randomly selected tree is at least as tall as hers.

 = Incorrect

Enter your answers as decimals accurate to 4 decimal places.

Answer 1

normal distribution

mean= 99.8

standard deviation = 5.4

x=100.9

z=(100.9- 99.8)/5.4= 1.1/5.4=.20370

use z tables or z calculator to find area under curve

one tail test, alpha =.05

P(x<100.9) = 58.071%=.5807

for neighbor's 104.1

z=(104.1- 99.8)/5.4 = 4.3/5.4 =.79630

P(x<104.1) = .78707 = .7871 rounded to 4 decimal places = 78.71% probability at most 104.1