The document provides solutions to calculating probabilities for a normally distributed random variable X with a mean of 80 and standard deviation of 5.
(1) It finds the probability that X is greater than 95 by converting to the standard normal variable Z and using normal distribution tables.
(2) It calculates the probability that X is less than 72 by again converting to Z and using tables.
(3) It determines the probability that X is between 60.5 and 90 by breaking it into separate probabilities and adding the areas under the normal curve.
2. Problem
If the random variable X is normally distributed
with mean 80 and standard deviation 5, then
find
a) P(X>95)
b) P(X<72)
c) P(60.5<X<90)
d) P(85<X<97) and
e) P(64<X<76)
3. Given Information
Here we are given that
μ = 80
σ = 5
X~N(80,25).
We know that is X~N(μ, σ²),then the S.N.V is given by
Z = X – μ
σ