Question

The lifetimes of light bulbs produced by a company are normally distributed with mean 1500 hours and standard deviation 125 hours.

(a) What is the probability that a single bulb will last at least 1400 hours?

(b) If three new bulbs are installed at the same time, what is the probability that they will all still be burning after 1400 hours? Assume the events are independent.

(c) If three new bulbs are installed at the same time, what is the probability that exactly two will be burning after 1400 hours?

(d) If three new bulbs are installed at the same time, what is the probability that at least two will be burning after 1400 hours?

Enter your answers as a decimal, not a percentage. Round to four decimal places.

Answer 1

Part a)

P ( X > 1400 ) = 1 - P ( X < 1400 )
Standardizing the value

Z = ( 1400 - 1500 ) / 125
Z = -0.8

P ( Z > -0.8 )
P ( X > 1400 ) = 1 - P ( Z < -0.8 )
P ( X > 1400 ) = 1 - 0.2119
P ( X > 1400 ) = 0.7881

Part b)

Part c)

Part d)

P ( X >= 2 ) = P ( X = 2 ) + P ( X = 3 )

P ( X >= 2 ) = 0.8843