The stem-and-leaf plot below shows the marathon training times (in minutes) fora random sample of 30 female runners. Training Times (in minutes) of Female Runners Key: 17|8 = 178 8 99 18 0 0 00 0 0 0 1 3 4 5 5 6 6 0 0 1 2 3 17 1 2 3 4 6 6 79 19 20 Provided the data from the stem-and-leaf plot above answer the following questions. 1. Use the sample to find a point estimate (round to 2 DP) for the mean training time of the female runners. 2. Find the sample standard deviation (round to 2 DP) of the training time for the female runners. 3. Use the sample to construct a 95% confidence interval for the population mean training time of the female runners. 4. Interpretthe result of Exercise 3. Write in complete sentences. 5. A trainer wants to estimate the population mean training time for female runners within 2 minutes. Determine the minimum sample size required to construct a 99% confidence interval for the population mean training time of female runners. Assume the population standard deviation is 8.4 minutes.

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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.