Based on a poll, 60% of Internet users are more careful about personal information when using a public Wi-Fi hotspot. What is the probability that among four randomly selected Internet users, at least one is more careful about personal information when using a public Wi-Fi hotspot? How is the result affected by the additional information that the survey subjects volunteered to respond? The probability that at least one of them is careful about personal information is

The probability that at least one of them is careful about personal information is 0.9744.

If the survey subjects volunteered to respond, then this a voluntary sampling and the estimated probability p may be biased, as only the people interested in the topic participate.

Given the subject of the survey, it is estimated that the ones who answered the survey are more careful about personal information and then the propability p is biased to a higher level than it should be if the sample was random.

Step-by-step explanation:

We can model this with a random variable, with sample size n=4 and probability of success p=0.6.

The probability that k individuals are more careful about personal information when using a public Wi-Fi hotspot in the sample is:

We have to calculate the probability that 1 or more are more careful about personal information when using a public Wi-Fi hotspot. This can be calculated as:

The probability that 1 or more individuals in the sample are more careful about personal information when using a public Wi-Fi hotspot is 0.9744.

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places