Final answer:
In probability and statistics, to determine how many residents will be surveyed before finding one with or without adequate earthquake supplies, one looks at the ratio of those who do or do not meet the criteria within the sample data. Probabilities and expected values are calculated accordingly, and for voter preferences, statistical hypothesis testing is conducted.
Step-by-step explanation:
The question relates to probability and statistics within the field of Mathematics and focuses on the analysis of survey data in a specific community in southern California for earthquake preparedness. According to the information provided, 511 homes were surveyed, with 173 meeting the minimum recommendations for earthquake preparedness, and 338 not meeting them.
To find a California resident who does not have adequate earthquake supplies, it is expected to need to survey one individual because the probability of finding such a resident in one survey is high, as 338 out of 511 homes did not meet the minimum recommendations.
Conversely, to find a resident who does have adequate earthquake supplies, more residents may need to be surveyed. The probability of encountering a home with adequate supplies in the first survey is 173/511, so it might take slightly longer to find one.
The probability that at least one or two residents must be surveyed to find one who does not have adequate earthquake supplies is the sum of the probabilities of it happening on the first try and the second try if it did not happen on the first. This can be calculated using the formula for such probabilities. Additionally, the probability that we must survey at least three residents until we find one who does not have adequate earthquake supplies is 1 minus the probability of finding one in the first two tries.
The part of the question about expecting how many will have adequate supplies and about the probability that at least eight have adequate supplies would require binomial probabilities to be calculated.
A separate question asked is related to a change in voter preferences after an earthquake. To answer this, a hypothesis test comparing the proportions before and after the earthquake, at a significance level of 0.05, would need to be performed to see if there has been a statistically significant change in voter distribution.