What is the proportion

Question

It is estimated that the mean life span of concrete drill bits is 20 hours. Suppose a construction company purchases drill bits that have a lifespan that is approximately normally distributed with a mean equal to 20 hours and and a standard deviation of 2 hours.

questions:

- What is the proportion of the company’s drill bits will fail before 18 hours of use?

- What is the proportion will last at least 18 hours?

- What proportion will have to be replaced after more than 25 hours of use?

Answer 1

x = hours of use, x normally distributed with mean = 20 and SD = 2.

want to find P(x < 18)

transform x to standard normal distribution using transformation z = x - mean / SD = x - 20 /2

P (x < 18) = P(z < 18-20/2) = P(z < -1) = 0.1587

P(x > 18) = 1 - P(x < 18) = 1 - 0.1587 = 0.8413

P(x > 25) = 1 - P(x < 25) = 1 - P(z < 25-20/2) = 1 - P(z < 2.5) = 1 - 0.9938 = 0.0062