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In a survey of U.S. adults, 16% say they have had someone take over their email accounts without their permission. You randomly select 250 U.S. adults and ask them whether they have had someone take over their email accounts without their permission.

Find the probability that the number of U.S. adults who say they have had someone take over their email accounts without their permission is:

a. At most 40

b. Less than 45

c. Exactly 48

Answer :

Final answer:

The question is about finding the binomial probabilities of a certain event - the probability of a U.S. adult having their email account taken over without their permission. The probabilities are calculated for at most 40, less than 45, and exactly 48 events.

Explanation:

This is a problem of binomial probability since we are looking at two outcomes (whether a U.S. adult has had someone take over their email account without their permission or not), where each outcome is independent of the other.

Let's denote X as a random variable that represents the number of U.S. Adults who have had someone take over their email accounts without their permission. Here, n = 250 (sample size), p = 0.16 (probability of success i.e., a person's email being taken over).

  1. At most 40: P(X <= 40)
  2. Less than 45: P(X < 45)
  3. Exactly 48: P(X = 48)

The binomial probability function can be used to calculate the above probabilities. The formula is P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k)), where C(n, k) is the number of combinations of n items taken k at a time.

Learn more about Binomial Probability here:

https://brainly.com/question/39666605

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Rewritten by : Barada

Answer:

a. At most 40

Step-by-step explanation:

If we take the survey that was done as a basis then we would use the 16% that was obtained as the number of overall US adults that have had their accounts used without their permission. Assuming that the 250 selected individuals were selected at random and without bias then those 250 would also be representative of the entire population. Therefore, we would simply need to multiply the number of selected individuals by the percentage in decimal form.

16 / 100 = 0.16

250 * 0.16 = 40

Finally, we can see that roughly 40 individuals would have had their email used without permission.