Question

It has been estimated that only about 15% of Caifornia residents have adequate earthquake supplies. Suppose we are interested in the number of California residents we must survey until we find a resident who does not have adequate earthquake supplies. Part (a) Part (b) Part (c) Part (d) Part (e) What is the probabity that we must survey at least 5 California resicents untl wo find a Cahifornia resident who does not have adequate earthquake supplies? (Round your answer fo four decimal paces.) x Part (f) Pant (g)

Answer 1

aFinal answer:

We use geometric distribution to calculate various probabilities related to surveying California residents for earthquake supplies. The expected number of residents to survey can be calculated using the mean of the distribution. Confidence intervals for population proportions come from sample proportions and associated statistical methods.

Step-by-step explanation:

The probability problem described involves waiting until finding a California resident with or without adequate earthquake supplies. Assuming the probability of a resident not having such supplies is 85%, the geometric distribution is used to calculate the probabilities. For instance, the probability of surveying exactly one or two residents before finding one without adequate supplies is computed by P(X = 1) or P(X = 2), where X represents the number of residents surveyed.

To calculate the expected number of residents needed to survey until finding one without adequate supplies, we use the mean of the geometric distribution which is 1/p, where p is the success probability (here 0.15 for those with supplies). Likewise, to find residents with supplies, the mean becomes 1/(1-p).

To answer the question 'What is the probability that we must survey at least 5 residents?', we apply this concept to calculate P(X ≥ 5). For the calculation of confidence intervals for populations surveying proportions, methods involving the sample proportion, standard error, and z-scores are applied.