Question

Based on previous studies, Australian residents change their electricity supplier on average three times every 10 years. i. What is the probability that a randomly chosen resident in Australia will change their electricity supplier just once in a given 10 year period? ii. What is the probability that a randomly chosen resident in Australia will change their electricity supplier more than nine times in a given 10 year period?

Answer 1

i. The probability that a randomly chosen resident in Australia will change their electricity supplier just once in a given 10-year period is approximately 0.268.

ii. The probability that a randomly chosen resident in Australia will change their electricity supplier more than nine times in a given 10-year period is very low, close to zero.

Step-by-step explanation:

In the first scenario (i), we can use the Poisson distribution, assuming a rate of λ = 0.3 (3 changes every 10 years). The probability of exactly one change is given by P(X = 1) = (e^(-0.3) * 0.3^1) / 1! ≈ 0.268. This indicates that about 26.8% of Australian residents are likely to change their electricity supplier exactly once in a 10-year period.

For the second scenario (ii), changing more than nine times in a 10-year period is an extreme event given the average rate. The Poisson distribution becomes highly skewed for larger values of X in this case, and the probability diminishes rapidly. As a result, the probability of changing more than nine times is effectively negligible, approaching zero.

In conclusion, the Poisson distribution provides a useful model for analyzing the probability of electricity supplier changes in Australia. It illustrates that a significant proportion of residents change just once in a 10-year period, while the likelihood of changing more than nine times is extremely low.