# Continuous probability

1. Oct 23, 2009

### tjera

I need help with this problem:
KleerCo supplies an under-hood, emissions-control air pump to the
automotive industry. The pump is vacuum powered and works while the
engine is operating, cleaning the exhaust by pumping extra oxygen into
the exhaust system. If a pump fails before the vehicle in which it is
installed has covered 50,000 miles, federal emissions regulations
require that it be replaced at no cost to the vehicle owner. The
company’s current air pump lasts an average of 63,000 miles, with a
standard deviation of 10,000 miles. The number of miles a pump
operates before becoming ineffective has been found to be normally
distributed.

a. For the current pump design, what percentage of the company’s pumps
will have to be replaced at no charge to the consumer?(P of X being smaller or equal to 50,000)

b. What percentage of the company’s pumps will fail at exactly 50,000
miles?(P of X being equal to 50,000)

c. What percentage of the company’s pumps will fail between 40,000 and
55,000 miles?(P of X being between those two values)

d. For what number of miles does the probability become 80% that a
randomly selected pump will no longer be effective?

I have found a,b,and c , but i don't know how to solve d. Since the value of Z is given,which is 0.80, i checked the Z scores table and tried to find a value close to 0,80 but i couldent see anything....

I would be forever grateful to someone who can help (i have an exam tomorrow !).

Thank You

2. Oct 24, 2009