The number of visitors to a particular website on a given day is approximately normally distributed with mean 5000 and variance 5002 . A company is considering placing an advertisement on this website. It predicts that each visitor to the website will order its product with probability 0.01, and that all visitors to the website act independently. (a) What is the expectation and variance of the number of orders the company receives? (b) Using a normal approximation, what is the probability that the number of orders the company receives is more than 100?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
The number of visitors to a particular website on a given day is approximately
(a) What is the expectation and variance of the number of orders the company receives?
(b) Using a normal approximation, what is the probability that the number of orders the company receives is more than 100?
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