In each problem, (a) identify the distribution, including the values of all para

Question

In each problem, (a) identify the distribution, including the values of all parameters, and (b) find the answer, to 4 decimal places.

5. A salesman notes that his success rate is about 10%. If he has 25 customers, and assuming independence, find the probability that he makes exactly 3 sales. A: B:

6. A batch of 20 computer monitors contains 4 defective ones. If you randomly select 5 monitors and test them, find the probability that you find at least one of the defective monitors. A: B:

7. Suppose that the expected number of customers at a convenience store is 6 every 20 minutes. In a given 20-minute time period, find the probability of having exactly 5 customers. A: B:

8. Find the probability that an investor makes a profit on 7 of her next 10 investments, assuming independence and a 0.6 chance of making a profit each time. A: B:

Explanation / Answer

5. A salesman notes that his success rate is about 10%. If he has 25 customers, and assuming independence, find the probability that he makes exactly 3 sales.

a. The binomial distribution describes the behavior of a count variable X if the following conditions apply:

1: The number of observations n is fixed.
2: Each observation is independent.
3: Each observation represents one of two outcomes ("success" or "failure").
4: The probability of "success" p is the same for each outcome.

So all the above conditions are satisfied, so this is binomial distribution.

b. Here p=0.10 and n=25

We need to find P(x=3)=ncx*p^x*(1-p)^n-x=0.2265

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