Question

1. the trees in a forest have a mean height of 39.5 feet with a standard deviation of 2.2 feet. assuming that the distribution of these trees has roughly the shape of a normal distribution, find:

a. the height below which are the shortest 30 percent of the trees

b. the height above which are the tallest 30 percent of the trees

Answer 1

µ = 39.5, σ = 2.2  

a) P(x < a) = 0.30

Z score at p = 0.30 using excel = NORM.S.INV(0.30) = -0.5244

Value of X = µ + z*σ = 39.5 + (-0.5244)*2.2 = 38.35

b) P(x > a) = 0.3  

= 1 - P(x < a) = 0.3  

= P(x < a) = 0.7  

Z score at p = 0.7 using excel = NORM.S.INV(0.7) = 0.5244

Value of X = µ + z*σ = 39.5 + (0.5244)*2.2 = 40.65