Question

The time spent by students working on this exam can be approximated by a normal random variable with mean value μ = 60 minutes and standard deviation σ = 5 minutes.

(a) What is the probability that a student finishes this exam in less than 50 minutes?

(b) What is the probability that a student spends between 60 minutes and 70 minutes taking this exam?

Answer 1

Part a)

X ~ N ( µ = 60 , σ = 5 )
P ( X < 50 )
Standardizing the value
Z = ( X - µ ) / σ
Z = ( 50 - 60 ) / 5
Z = -2
P ( ( X - µ ) / σ ) < ( 50 - 60 ) / 5 )
P ( X < 50 ) = P ( Z < -2 )
P ( X < 50 ) = 0.0228

Part b)

X ~ N ( µ = 60 , σ = 5 )
P ( 60 < X < 70 )
Standardizing the value
Z = ( X - µ ) / σ
Z = ( 60 - 60 ) / 5
Z = 0
Z = ( 70 - 60 ) / 5
Z = 2
P ( 0 < Z < 2 )
P ( 60 < X < 70 ) = P ( Z < 2 ) - P ( Z < 0 )
P ( 60 < X < 70 ) = 0.9772 - 0.5
P ( 60 < X < 70 ) = 0.4772