The expected (mean)life of a particular type of light bulb is 1,000 hours with a standard deviation of 50 hours.The life of this bulb is normally distributed.What is the probability that a randomly selected bulb would last less than 1,100 hours?
A)0.4772
B)0.9772
C)0.0228
D)0.5228
E)0.5513

Question

Quizplus · Accepted Answer

From the given information, we know that the population mean is 1000 hours and the population standard deviation is 50 hours. We want to find the probability that a randomly selected bulb would last less than 1100 hours.
Using the formula for standardized normal distribution: 
z = (x - μ) / σ 
where x is the value we want to find the probability for, μ is the population mean, and σ is the population standard deviation.
Plugging in the values, we get: 
z = (1100 - 1000) / 50 = 2
Using a standard normal distribution table or calculator, we find that the probability of a z-score less than 2 is 0.9772. So the probability that a randomly selected bulb would last less than 1100 hours is 0.9772 or 97.72%. Therefore, the best choice is (B).

The Expected (Mean)life of a Particular Type of Light Bulb