Refer to the chapter-opening Case Study on page 000. The bank manager wants to know whether or not the bank's customer service agents generally met the goal of answering incoming calls in less than 30 seconds. We can approach this question in two ways: by estimating the proportion p of all calls that were answered within 30 seconds or by estimating the mean response time u. Some graphs and numerical summaries of the data are provided below. 2- 20 40 Call response time (reeonds) 150 225 100 s75 450 7.5 Call response time (seconds) Descriptive Statistics: Call response time (sec) Variable N Mean SE Mean StDev Minimum QI 241 18.353 0.758 11.761 1.000 9.000 Call response time (sec) 1. Describe the distribution of call response times for the random sample of 241 calls. 2. About what proportion of the call response times in the sample were less than 30 seconds? Explain how you got your answer. 3. The bank's manager would like to estimate the true proportion p of calls to the bank’s customer service center that are answered in less than 30 seconds. (a) What conditions must be met to calculate a 95% confidence interval for p? Show that the conditions are met in this case. (b) Explain the meaning of 95% confidence in this setting. (c) A 95% confidence interval for p is (0.783, 0.877). Give the margin of error and show how it was calculated. iouanbaag

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Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.