Answer
$P(22\le X\le27)=0.2415$
Work Step by Step
Let's find the z-scores for 22 and 27:
$z=\frac{X-μ}{σ}=\frac{22-20}{3}=0.67$
$z=\frac{X-μ}{σ}=\frac{27-20}{3}=2.33$
According to Table V, the area of the standard normal curve to the left of z-score equal to 0.67 is 0.7486.
According to Table V, the area of the standard normal curve to the left of z-score equal to 2.33 is 0.9901.
The area of the standard normal curve between the z-scores 0.67 and 2.33 is the difference between the area of the standard normal curve to the left of z-score equal to 2.33 and the area of the standard normal curve to the left of z-score equal to 0.67:
$0.9901-0.7486=0.2415$
