Final answer:
The number of California residents with adequate earthquake supplies can be modeled with binomial and geometric distributions, with 30 percent estimated to be prepared. Point estimates are derived from surveys, such as a sample of 511 homes where 173 were adequately prepared. Probabilities of finding prepared or unprepared residents can be calculated using these distributions.
Step-by-step explanation:
The question pertains to the estimation of how many California residents have adequate earthquake supplies. Given that it's been estimated that only about 30 percent of California residents have adequate supplies, we can utilize this statistic to make calculations about the expected number of residents with adequate supplies. For instance, if we were to survey 11 residents, we could model the number who have adequate supplies using a binomial distribution, where the random variable X represents the number of residents with adequate supplies out of the 11 surveyed.
A point estimate for the proportion of homes that do not meet minimal earthquake preparedness recommendations can be obtained from survey data. For example, if 511 homes were surveyed and 173 met the minimum recommendations, we have 511 - 173 = 338 homes that do not, yielding a point estimate of 338/511.
As for the probability that we must survey a certain number of residents until we find one without adequate supplies, we can use the concept of geometric distribution. The random variable X in this context defines the number of trials until the first success, where 'success' is defined as finding a resident without adequate supplies. Given the provided statistics, we can calculate these probabilities for different scenarios.