1. A bank is conducting a customer satisfaction survey, sampling from a list of 25000 active customers. The list includes 15000 general account holders, 5000 community-care account holders, 2500 premium account holders and 2500 enterprise account holders. The analyst would like to obtain a sample of 500 customers by random sampling. (a) The selection will be made so that there is as close a representation as possible without bias towards any group of customers (i) What sampling method should be used? (ii) How many community-care account holders should be selected? (b) If systematic sampling is used to select the samples in the general customer account holders (i) What is the sampling interval? (ii) If the first sample taken is 00028, suggest the third and fourth codes for the next two samples 2. The spending of 20 customers on movies and snacks are as follows: 110 122 132 163 120 114 168 129 148 141 135 155 131 152 147 148 136 167 153 157 (a) Draw the stem-and-leaf diagram for these data e (b) Find the median, the lower and the upper quartiles of the data (c) Find the sample variance and the sample standard deviation of the data. (d) Comment briefly on the skewness of the data.

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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.