Question

The time it takes for robots to defect is normally distributed with a mean time of 1,500 hours and a standard deviation of 120 hours.

a) What is the probability that a robot will ‘break down’ before 1680 hours?
b) What is the probability that a robot breaks down between 1380 hours and 1590 hours?

Answer 1

Part a)

X ~ N ( µ = 1500 , σ = 120 )
P ( X < 1680 )
Standardizing the value
Z = ( X - µ ) / σ
Z = ( 1680 - 1500 ) / 120
Z = 1.5
P ( ( X - µ ) / σ ) < ( 1680 - 1500 ) / 120 )
P ( X < 1680 ) = P ( Z < 1.5 )
P ( X < 1680 ) = 0.9332

Part b)

X ~ N ( µ = 1500 , σ = 120 )
P ( 1380 < X < 1590 )
Standardizing the value
Z = ( X - µ ) / σ
Z = ( 1380 - 1500 ) / 120
Z = -1
Z = ( 1590 - 1500 ) / 120
Z = 0.75
P ( -1 < Z < 0.75 )
P ( 1380 < X < 1590 ) = P ( Z < 0.75 ) - P ( Z < -1 )
P ( 1380 < X < 1590 ) = 0.7734 - 0.1587
P ( 1380 < X < 1590 ) = 0.6147