Question

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 longer than 1150 hours? 0.9987 0.0013 0.5013 0.5513 0.4987

Answer 1

Answer:

Option B) 0.0013

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 1000 hours

Standard Deviation, σ = 50 hours

We are given that the distribution of life of bulb is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

P(bulb would last longer than 1150 hours)

$P( x > 1150) = P( z > \displaystyle\frac{1150 - 1000}{50}) = P(z > 3)$

$= 1 - P(z \leq 3)$

Calculation the value from standard normal z table, we have,  

$P(x > 1150) = 1 - 0.9987 = 0.0013$

0.0013 is the probability  that a randomly selected bulb would last longer than 1150 hours.

Thus, the correct answer is

Option B) 0.0013