Question

4) The lifetime in hours) of a certain type of light bulb is approximately normal with a mean of 1,000 hours and a standard deviation of 70 hours. What is the probability that the bulb will last between 1050 and 1150 hours? Assume normal distribution. Solve the problem in two (2) completely different ways * 1 way using normal table and 1 way NOT using normal table. (9 marks)

Answer 1

4.

the PDF of normal distribution is = 1/σ * √2π * e ^ -(x-u)^2/ 2σ^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd ~ N(0,1)
mean ( u ) = 1000
standard Deviation ( sd )= 70

probability that the bulb will last between 1050 and 1150 hours.
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 1050) = (1050-1000)/70
= 50/70 = 0.7143
= P ( Z <0.7143) From Standard Normal Table
= 0.7625
P(X < 1150) = (1150-1000)/70
= 150/70 = 2.1429
= P ( Z <2.1429) From Standard Normal Table
= 0.9839
P(1050 < X < 1150) = 0.9839-0.7625 = 0.2215