Respuesta :
Answer:
The probability that a randomly chosen tree is greater than 140 inches is 0.0228.
Step-by-step explanation:
Given : Cherry trees in a certain orchard have heights that are normally distributed with [tex]\mu = 112[/tex] inches and [tex]\sigma = 14[/tex] inches.
To find : What is the probability that a randomly chosen tree is greater than 140 inches?
Solution :
Mean - [tex]\mu = 112[/tex] inches
Standard deviation - [tex]\sigma = 14[/tex] inches
The z-score formula is given by, [tex]Z=\frac{x-\mu}{\sigma}[/tex]
Now,
[tex]P(X>140)=P(\frac{x-\mu}{\sigma}>\frac{140-\mu}{\sigma})[/tex]
[tex]P(X>140)=P(Z>\frac{140-112}{14})[/tex]
[tex]P(X>140)=P(Z>\frac{28}{14})[/tex]
[tex]P(X>140)=P(Z>2)[/tex]
[tex]P(X>140)=1-P(Z<2)[/tex]
The Z-score value we get is from the Z-table,
[tex]P(X>140)=1-0.9772[/tex]
[tex]P(X>140)=0.0228[/tex]
Therefore, the probability that a randomly chosen tree is greater than 140 inches is 0.0228.
