normal distribution using Z - finding probability between 2 numbers

Question

I am wanting to find the probability of the following: SD = 20 Mean = 100

P(85 < X < 117)

i have found the z values for both:

P(X>85) : X-u/o = 85-100/20 Z = -0.75 and found the probability for this to be: P(X>85) = 1-P(X<85) = 1-0.2266 = 0.7734

P(X<117) : Z = X-u/o = 117-100/20 Z = 0.85 and the probability = 0.8023

so have the probabilities for both conditions but how do I get P(851 so how would I find this probability?

Answer 1

To find $P(85<X<117)$ is the same as finding $P(X<117)-P(X<85)$.

Answer 2

As Joe said, It is the the probability that X is less than 117 minus the probability that X is less than 85. You can think of it as the area under the curve between these two points. I hope that helps!