Question

The 70 highest dams in the world have an average height of 206 meters with a standard deviation of 35 meters. the hoover and grand coulee dams have heights of 221 and 168 meters, respectively. the russian dams, the nurek and charvak, have heights with z-scores of +2.69 and – 1.13, respectively. list the dams in order of ascending size.

Answer 1

Given:
μ = 206 m, the mean
σ = 35 m, the standard deviation.

By definition, the z-score for the random variable ,x, is
z = (x - μ)/σ
Therefore,
x = μ + σz

The heights of the given dams are
Hoover: 
  x = 221 m
Grand Coulee:
  x = 168 m
Nurek: 
  z = 2.69
  x = 206 + 35*2.69 = 300.15 m
Hoover: 
  z = -1.13
  x = 206 - 35*1.13 = 166.45 m

Answer:
In ascending order of x, the dams are
Charvak
Grand Coulee
Hoover
Nurek