Answer
$P(65\lt X\lt 85)=0.6247$
Work Step by Step
Let's find the z-scores for 65 and 85:
$z=\frac{X-μ}{σ}=\frac{65-70}{10}=-0.5$
$z=\frac{X-μ}{σ}=\frac{85-70}{10}=1.5$
According to Table V, the area of the standard normal curve to the left of z-score equal to -0.5 is 0.3085.
According to Table V, the area of the standard normal curve to the left of z-score equal to 1.5 is 0.9332.
The area of the standard normal curve between the z-scores -0.5 and 1.5 is the difference between the area of the standard normal curve to the left of z-score equal to 1.5 and the area of the standard normal curve to the left of z-score equal to -0.5:
$0.9332-0.3085=0.6247$
