Lots of 40 components each are deemed unacceptable if they contain 3 or more defectives. The procedure for sampling a lot is to take 5 components at random and to reject the lot if a defective is found. What is the probability that exactly 1 defective is found in the sample if there are 3 defectives in the entire lot? What is the probability that this lot will be rejected?

A manufacturer of automobile tires reports that among a shipment of 5000 sent to a local distributor, 1000 are slightlly blemished. If one purchase 10 of these tires at random from the distributor, what is the probability that exactly 3 are blemished?

Example 6.1: Suppose that a large conference room at a certain

company can be reserved for no more than 4 hours. Both long and

short conferences occur quite often. In fact, it can be assumed

that the length X of a conference has a uniform distribution on 

the interval [0, 4].

(a) What is the probability density function?

(b) What is the probability that any given conference lasts at least

3 hours?

Solution : (a) The appropriate density function for the uniformly