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dlinn [17]
2 years ago
6

Software filters rely heavily on ""blacklists"" (lists of known ""phishing"" URLs) to detect fraudulent e-mails. But such filter

s typically catch only 20 percent of phishing URLs. Jason receives 16 phishing e-mails. (a) What is the expected number that would be caught by such a filter? (Round your answer to 1 decimal place.) Expected number (b) What is the chance that such a filter would detect none of them? (Round your answer to 5 decimal places.) Probability
Mathematics
1 answer:
crimeas [40]2 years ago
6 0

Answer:

a) X \sim Binom(n=16, p=0.2)  

The probability mass function for the Binomial distribution is given as:  

P(X)=(nCx)(p)^x (1-p)^{n-x}  

Where (nCx) means combinatory and it's given by this formula:  

nCx=\frac{n!}{(n-x)! x!}  

The expected value is given by this formula:

E(X) = np=16*0.2=3.2

b) P(X=0)=(16C0)(0.2)^{0} (1-0.2)^{16-0}=0.02815

Step-by-step explanation:

Previous concepts  

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".  

Part a

Let X the random variable of interest, on this case we now that:  

X \sim Binom(n=16, p=0.2)  

The probability mass function for the Binomial distribution is given as:  

P(X)=(nCx)(p)^x (1-p)^{n-x}  

Where (nCx) means combinatory and it's given by this formula:  

nCx=\frac{n!}{(n-x)! x!}  

The expected value is given by this formula:

E(X) = np=16*0.2=3.2

Part b

For this case we want this probability:

P(X=0)

The probability mass function for the Binomial distribution is given as:  

P(X)=(nCx)(p)^x (1-p)^{n-x}  

Where (nCx) means combinatory and it's given by this formula:  

nCx=\frac{n!}{(n-x)! x!}  

And using this function we got:

P(X=0)=(16C0)(0.2)^{0} (1-0.2)^{16-0}=0.02815

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Step-by-step explanation:

Hello!

Hannah estimated per CI the difference between the average time that people spend outside in southern states and the average time people spend outside in northern states.

The CI is a method of estimation of population parameters that propose a range of possible values for them. The confidence level you use to construct the interval can be interpreted as, if you were to calculate 100 confidence interval, you'd expect that 99 of them will contain the true value of the parameter of interest.

In this example, the 99%CI resulted [0.4;8.0]hs

Meaning that with a 99% confidence level you'd expect the value of the difference between the average time people from southern states spend outside than the average time people from northern states spend outside is included in the interval [0.4;8.0]hs.

Now, she claims that people living in southern states spend 9 more hours outside than people living in northern states, symbolized μ₁ - μ₂ > 9

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Step-by-step explanation:

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Answer:

s = -2400t + 17400

Step-by-step explanation:

Let's say t is the x value on a coordinate plane, and s is the y. Then, we have the points (0, 17400) and (6, 3000). The slope of these is 14400/-6 or -2400.

Now we just have the equation y = -2400x + b, and from the point (0, 17400) we can find that b is 17400. So, we have y = -2400x + 17400. Convert these back into t and s and you get your answer, s = -2400t + 17400.

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