Question

It has been estimated that only about 30% of california residents have adequate earthquake supplies. suppose you randomly survey 13 california residents. we are interested in the number who have adequate earthquake supplies. part (a) part (b) part (c) part (d) what is the probability that at least seven have adequate earthquake supplies? (round your answer to four decimal places.)

Answer 1

The probability that at least seven out of 13 California residents have adequate earthquake supplies is 0.2242.

Step-by-step explanation:

In this scenario, we can use the binomial probability formula to calculate the probability. The formula for binomial probability is P(X = k) = (n choose k)
`p^k^ ^(1-p)^(n-k),` where n is the number of trials, k is the number of successes, and p is the probability of success on an individual trial. In this case, n = 13, k ≥ 7, and p = 0.30.

We need to find the probability of having at least seven residents with adequate earthquake supplies, so we calculate P(X ≥ 7) = P(X = 7) + P(X = 8) + … + P(X = 13). Using this formula and performing the calculations, we find that the probability is 0.2242.

This result indicates that there is a relatively low likelihood that at least seven out of 13 California residents have adequate earthquake supplies based on the estimated percentage. It underscores the importance of raising awareness about earthquake preparedness and encouraging more residents to have sufficient supplies in case of such a natural disaster.

It’s crucial for individuals and communities to prioritize preparedness for potential earthquakes, as they can strike without warning and have devastating consequences. By understanding the probabilities involved and taking proactive measures to ensure adequate supplies, residents can better protect themselves and their families in the event of an earthquake.