The heights of Mr McDonalds dwarf peach trees are normally d

The heights of Mr. McDonald’s dwarf peach trees are normally distributed with a mean of 65 inches and a standard deviation equal to 3 inches.About what proportion of his trees are between 65 and 67 inches?

Solution

Given X~N(65,3) , when X=65, Z=(X-)/=(65-65)/3=0 X=67, Z=(67-65)/3=2/3=0.67. Then P(65<=X<=67)=P(0<=Z<=0.67)=0.2486(By the Z table values).