To find the shaded area we first find the area from 165cm to 175cm because we always
measure standard deviations from the mean. Using the z equation
z = X - u = 165 - 175 = -10 = -1.67
The table value for the area under the normal curve corresponding to -1.67 standard deviations
from the mean is .4525. The total area to the left of the mean is .5000, so the area of interest is .
5000- .4525 = .0475 (4.75%). Thus, we can expect 475 (.0475 X 10,000 - 475) recruits to require
Size A uniforms.
For Size B the area of interest would be:
u - 175
We already know that 165cm is -1.67 standard deviations from the mean, so 45.25% of the area
under the curve lies between the mean and 165cm. Finding the area under the curve between the
mean and 173cm will allow us to solve the problem. Using the z equation:
z = X - u = 173 - 175 = -2 = -.33