Andy is a restaurant owner. He believes 71% of his customers...

Andy is a restaurant owner. He believes 71% of his customers are satisfied with the food quality of his restaurant. From a random sample of 97 customers, what are the following probabilities? (Round your answers to four decimal places, if needed.) (a) What is the probability that less than 70 customers are satisfied with the food quality? (b) What is the probability that at least 70 customers are satisfied with the food quality? (c) What is the probability that the sample proportion of customers who are satisfied with the food quality is between 69% and 75%?

Transcript

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

00:03 In the question here, we are going to discuss about the summary distribution of the sample proportion.

00:08 Let me remind you that under certain condition, the sample proportion p heart will be approximately to the normal.

00:14 Where we have the mean of the pht equal to the p, standard division of pht equal to the square root of the p times 1 minus p over n.

00:23 And because a pht follows by the normal, everything the p hath means minus the mu, development by the standard deviation.

00:31 We have 10 standard normal.

00:33 In the question here, we have the p, it will be the 71 % of the customer are satisfied with the food quality.

00:39 So it will be the 171, the symbol and equal to the 97.

00:44 So therefore we have the p hat will be approximately to the normal.

00:48 Well, we have the mean on the p equal to the 771 and we have the sigma of the phe equal to the square root of 0 .171, 1 minus 171 over the 97.

01:04 Then we get equal to 97, i mean 97, taking the square root, equal to the 046.

01:13 Now we are ready to answer the first question a.

01:16 Once you find the probability that less than 70 customers are certified, so x will be less than 70.

01:23 To find this probability, we divide both sides by n, which is equal to the 97.

01:28 Then, then, then the quantity on the left here it turns out to be the p heart and 70 divided by 97 equal to the 1722.

01:39 And then i have to confirm the p heart here into the z by using the formula here.

01:45 Then we take the zabon 722 minus the mean, divided by the standard deviation.

01:52 And if we compute we have the z will be smaller than minus z 171, divide.

01:59 By 046 equal to the 0253...

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