Question: A zoo in a major city is contemplating whether to install a digital system, which will allow the visitors to get information about a particular attraction at the touch of a digital code through a device they will rent. It is anticipated that this device will rent for $3 each. Based on this rental price, a financial analyst for the zoo indicates that if more than 10% of the zoo visitors rent the system, the rental revenue will more than offset the installation cost of the system and the zoo will make a profit. To help make the decision, a random sample of 400 zoo visitors were given the details of the system capabilities and rental cost and were asked whether they will rent such a device or not.

(a) If 45 people say that they will rent such a device, construct a 98% confidence interval for the proportion (p) of the zoo visitors who will rent this device. What does this interval means?

(b) Based on your answer to part (a), can you say with confidence that the installation of this system will be a financial success for the zoo? Discuss.

(c) If the zoo will like the margin of error to be only .02 (2%), how many more visitors should be surveyed?