5) A salesperson has found that the probability of a sale on a single contact is 0.05. a) Calculate the exact probability that, if the salesperson contacts 100 prospects, she will make at least four sales. b) If the salesperson contacts 100 prospects, use both of the methods we have discussed to calculate the approximate probability that she will make at least four sales. Which of the methods produces the more accurate approximation

And if we replace we got:

So we expect about 0.8 defective computes in a batch of 4 selected.

Step-by-step explanation:

Previous concepts

The expected value of a random variable X is the n-th moment about zero of a probability density function f(x) if X is continuous, or the weighted average for a discrete probability distribution, if X is discrete.

Solution to the problem

For this case we have the following distribution given:

X           0             1               2               3             4

P(X)  0.4096    0.4096    0.1536    0.0256    0.0016

And we satisfy that and so we have a probability distribution. And we can find the expected value with the following formula:

And if we replace we got:

So we expect about 0.8 defective computes in a batch of 4 selected.