Question

Suppose a random individual is obtained from a population with μ=64 and σ=15. Find the probability of

A. P(x>65.5)=?

B. ​P(x<67.7)=?

C. ​P(64.3<x<65.65)=?

Answer 1

X follows normal distribution mean μ and standard deviation σ    
Given μ = 64  σ = 15
     
A) To find P(X > 65.5)    
P(X > 65.5) = 1 - P(X ≤ 65.5)    
We find these probability using Excel function NORM.DIST    
P(X > 65.5) = 1 - NORM.DIST(65.5, 64, 15, TRUE)    
                = 1 - 0.5398    
                = 0.4602    
P(X > 65.5) = 0.4602   
     
B) To find P(X < 67.7)    
We find these probability using Excel function NORM.DIST    
P(X < 67.7) = NORM.DIST(67.7, 64, 15, TRUE)    
                = 0.5974    
P(X < 67.7) = 0.5974    
     
C) To find P(64.3 < X < 65.65)    
P(64.3 < X < 65.65) = P(X < 65.65) - P(X < 64.3)    
We find these probability using Excel function NORM.DIST    
P(64.3 < X < 65.65) = NORM.DIST(65.65, 64, 15, TRUE)     
                                               - NORM.DIST(64.3, 64, 15, TRUE)  
                = 0.5438 - 0.5080    
                = 0.0358    
P(64.3 < X < 65.65) = 0.0358