It has been reported that 60% of all internet users have been attacked by viruse

Question

It has been reported that 60% of all internet users have been attacked by viruses. If 16 people are randomly surveyed, find the following probabilities: a. At least 6 have been attacked b. No more than 4 have been attacked c. Less than 13 have been attacked
It has been reported that 60% of all internet users have been attacked by viruses. If 16 people are randomly surveyed, find the following probabilities: a. At least 6 have been attacked b. No more than 4 have been attacked c. Less than 13 have been attacked
It has been reported that 60% of all internet users have been attacked by viruses. If 16 people are randomly surveyed, find the following probabilities: a. At least 6 have been attacked b. No more than 4 have been attacked c. Less than 13 have been attacked

Explanation / Answer

60% of all internet users have been attacked by viruses.

Let X = number of internet users have been attacked by viruses

n = sample size = 16

Here n is fixed, probability of success = p = 0.60

trials are independent with two outcomes as success and failure.

So we can used binomial distribution to find the probability.

a) For the phrase " at least" we need to find greater than or equal to probability.

Mathematically,

P( X >= 6) = 1 - P(X < = 5).....(1)

By using excel:

P( X <= 5) = "=BINOMDIST(5,16,0.6,1)" = 0.019142

Plug this value in equation 1, we get

P( X >= 6) = 1 - 0.019142 = 0.980858

b) P( no more than 4 ) = P( X less than or equal to 4) = P( X <= 4) = "=BINOMDIST(4,16,0.6,1)" = 0.004896

c) P( Less than 13 ) = P( X < 13) = P( X <= 13 -1) = P( X < = 12) = "=BINOMDIST(12,16,0.6,1)" =0.934853

{Note that the general command to find cumulative(less than equal to ) binomial

probabilities in excel is "==BINOMDIST(x,n,p,1)}

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