Find: P(38< = X < = 45 when mu = 40, sigma = 2.5

Question

Find: P(38< = X < = 45 when mu = 40, sigma = 2.5

 

does the below answer look accurate..calculated in excel

 

Probability for a Range
From X Value 38
To X Value 45
Z Value for 38 -0.8
Z Value for 45 2
P(X<=38) 0.2119
P(X<=45) 0.9772
P(38<=X<=45) 0.7654

Answer 1

Prob ( 38 <= X <= 45) = 

 

Prob ( (38-40)/2.5 <= z <= (45-40)/2.5) =

 

prob( -0.8 <= z <= 2)

 

= prob( z <= 2) - prob( z <= -0.8)

 

= 0.9772 - 0. 2119

 

=0.7653