Suppose that 3 out of every 10 homeowners in the state of...

Suppose that 3 out of every 10 homeowners in the state of California has invested in earthquake insurance. Suppose 20 homeowners are randomly chosen to be interviewed. (a) What is the probability that at least one had earthquake insurance? (Round your answer to three decimal places.) (b) What is the probability that four or more have earthquake insurance? (Round your answer to three decimal places.) (c) Based on the empirical rule within what limits would you expect the number of homeowners insured against earthquakes to fall approximately 95% of the time? (Round your answers to the nearest whole number.)

Transcript

00:01 Hi, i'm david and i'm here to help you answer your question.

00:04 Now let me bring up your question here.

00:07 In this question here, we're going to discuss about the binomial distribution.

00:11 Let me remind you that if we have the x that followed by the binomial with the n and the p.

00:18 And then the probability of the x equal to k equal to n twosk, b power k times 1 minus b power n minus k.

00:32 And also the mean of the x will equal to the mule and equal to the n times b.

00:40 The standard division it will equal to the square root of the n times b times 1 minus b.

00:47 In this question here we given 3 out of 10 of the homeowners in the state of california has invested in the earthquake insurance.

00:56 So the b here will be equal to the 3 out of 10, so it will equal to the 0 .3 .3.

01:01 Now we have the symbol n equal to the 20 homeowners.

01:08 So if we call the x, it would equal to the number of the homeowner that invest in the earthquake insurance.

01:28 And then we will see the x here, it will follow by the binomial with the n equal to the 20 and the p equal to the 7 -3.

01:38 Now the question i asked not to find the probability that alice 1 had the earthquake insurance so probability the x equal at least one will be greater equal to 1 to find this probability just equal to 1 minus probability in the x equal to 0 and it will apply the formula here we'll get equal to the 20 we choose 0 be equal to the 0 .3 power 0 1 minus 0 1 3 will be the 0 1 7 power 20 minus 0 will be the 20 now it will compute this one we get the answer so let me compute here for you 0 .3 and then 20 and this one will be the 0 so get equal to the 0 .00 79 and that's will be the end i will run up to the 80 here now that's going to be the answer for the a now for the b once you find the probability that for or more so x will be greater equal to the 4.

02:53 Now to find this probability is equal to the summation k goes from 4 up to the 20 and then the formula will be the 20 we choose k and then 0 .3 power k 0 .7 power 20 minus k and then if we compare this one pretty equal to the 4 we get equal to the 01829 and now for the question c we need to use the importance to find the 95 % confident interval...

Question

Please give Ace some feedback