# In a restaurant chain the proportion of people who

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In a restaurant chain, the proportion of people who order coffee with their dinner is 0.9. A simple random sample of 144 patrons of one of the restaurants in the chain is taken.h. Based only on a sample of 200 patrons of one of the restaurants in the chain showing that 170 patrons ordered coffee with their dinner, what can the restaurant conclude?
i. Assuming the proportion for the chain is true for the one restaurant sample, what is the probability that less than 127 of the customers in the sample ordered coffee with their dinner?j. Assuming the proportion for the chain is true for the one restaurant sample, what is the probability that the proportion of customers at this restaurant who order coffee with their dinner is at least 95%?k. Describe the random variable for the probability distribution used to answers parts i and j (i.e., what type of variable, what is the probability distribution, what does the variable represent, what are it's possible values, etc.).
l. The the proportion of 0.9 is true for this one restaurant in the chain, within what range would you expect to find 95% of all sample proportions of customers at the restaurant who order coffee with dinner?m. If the sample from the restaurant shows 137 customers ordered coffee with dinner, based on your answer in part l, explain what might be concluded.