Answer:
97.5 %
15.7 %
Step-by-step explanation:
[tex]\mu[/tex] = Mean = 19
[tex]\sigma[/tex] = Standard deviation = 2.3
a)
[tex]\mu+x\sigma=25.9\\\Rightarrow 19+x\times 2.3=25.9\\\Rightarrow x=\frac{25.9-19}{2.3}\\\Rightarrow x=3[/tex]
[tex]\mu-x\sigma=14.4\\\Rightarrow 19-x\times 2.3=14.4\\\Rightarrow x=\frac{19-14.4}{-2.3}\\\Rightarrow x=2[/tex]
From the empirical rule we get that the percentage of trees between 14.4 and 25.9 inches is 13.6+34.1+34.1+13.6+2.1 = 97.5 %
b)
[tex]\mu+x\sigma=21.3\\\Rightarrow 19+x\times 2.3=21.3\\\Rightarrow x=\frac{21.3-19}{2.3}\\\Rightarrow x=1[/tex]
The fraction of tree under 21.3 inches is 34.1.
Hence the fraction of trees above the diameter of 21.3 inches is 13.6+2.1 = 15.7 %
