1. New regulations in Canada require all Internet service providers (ISPs) to se
ID: 2949497 • Letter: 1
Question
1. New regulations in Canada require all Internet service providers (ISPs) to send a notice to subscribers who are downloading files illegally asking them to stop. This “notice and notice” system was already in place with Rogers Cable. That company says that prior to these new regulations, 67% of its subscribers who received a notice did not reoffend.18 Consider a random sample of 50 of these Rogers subscribers who received a first notice.
What is the distribution of the number X of subscribers who reoffend? Explain your answer.
What is the probability that at least 18 of the 50 subscribers in your sample reoffend?
2. Refer to question 1. Given the new regulations, suppose that 75% of the Canadian ISP subscribers will not reoffend after receiving a notice.
If you choose at random 15 subscribers who received a notice, what is the mean of the count X who will not reoffend? What is the mean of the proportion ˆp in your sample who will not reoffend?
Repeat the calculations in part (a) for samples of size 150 and 1500. What happens to the mean count of successes as the sample size increases? What happens to the mean proportion of successes?
Explanation / Answer
Q-1.
probability of success ---> the percents they do not reoffend. In this case(i.e. 67%). The sample size-----> 50. Use dbinorm function to draw the distribution:
With the probability of 67%, the probability of success displays as a bell shaped curve, with the mean around 35. The curve started to raise at 23 and end at 49. Very few probabilities lie outside this range. In this case, with the sample of 50 people, around 35 people will not reoffend after the first notice.
Probability that at least 18 of the 50 subscribers in your sample reoffend
This is calculated by summing all the binomial probability from 18 to 50 subscribers who will not reoffend and subtracting it by 1:
So, 0.0000012 of subscribers will reoffend.
Q-2.
Here the probability of success (p), which is the percents that subscribers will not reoffend, is 75%. Random sample of 15 subscribers.
the mean of the count X is approximately 11. However, to be precise, the mean value of the binomial distribution is calculated by multiplying the sample size (n = 15) by the probability of success (0.75);
So, the mean of the count X who will not reoffend is 11.25. This mean that out of 15 people, about 11 people will not reoffend.
For samples of size 150 and 1500.
We can calculate the mean count of successes either by drawing the graphs or by calculating using formula. calculate the mean by multiplying the probability of successes by the sample size:
These numbers show that the mean for sample sizes of 150 is 112.5, while the mean with sample sizes of 1500 is 1125.
mean proportion of successes
The mean proportion of successes is equal to the mean of the count of success divided by the sample sizes, which is exactly 75%:
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