The heights of Mr McDonalds dwarf peach tree are normally di

The heights of Mr. McDonald\'s dwarf peach tree are normally distributed with a mean of 65 inches and a standard deviation equal to 3 inches. About what proprotion of his trees are between 65 and 67 inches? 0.7486 0.5000 0.2486 0.1700 0.8300 15 percent of Mr. McDonald\'s trees are taller than x inches. The value of x is 61.89 68.12 70.11 63.89 60.07

Solution

Normal Distribution
Mean ( u ) =65
Standard Deviation ( sd )=3
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 65) = (65-65)/3
= 0/3 = 0
= P ( Z <0) From Standard Normal Table
= 0.5
P(X < 67) = (67-65)/3
= 2/3 = 0.6667
= P ( Z <0.6667) From Standard Normal Table
= 0.74751
P(65 < X < 67) = 0.74751-0.5 = 0.2486                  

b)
P ( Z > x ) = 0.15
Value of z to the cumulative probability of 0.15 from normal table is 1.04
P( x-u/ (s.d) > x - 65/3) = 0.15
That is, ( x - 65/3) = 1.04
--> x = 1.04 * 3+65 = 68.12