Over the past decade, the mean number of hacking attacks experienced by members of the Information Systems Security Association is 510 per year with a standard deviation of 14.28 attacks. The distribution of number of attacks per year is normally distributed. Suppose nothing in this environment changes. 1. What is the possibility they will experience an average of less than 500 attacks over the next 10 years? 2. Compute the probability the mean number of attacks over the next 10 years is between 500 and 600.
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!
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Over the past decade, the |
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1. What is the possibility they will experience an average of less than 500 attacks over the next 10 years? |
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2. Compute the |
Solution:
Let X be the number of attacks per year.
From the given information, X follows normal distribution with mean µ=510 per year and a standard deviation σ=14.28 attacks.
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