114 61. The average heart rate for adults is 72 bpm with standard deviation of 6bpm. The distribution of heart rates is Normal. (a) What is the probability that a randomly selected heart rate is less than 60 bpm? (b) What is the probability that a randomly selected heart rate is between 70 and 80 bpm? (c) What is the 40th percentile of heart rates? 62. A particular bakery makes a very popular peanut butter pie. Suppose daily demand follows a Normal distribution with mean 43 pies and standard deviation 5 pies. (a) What is the probability that the demand is between 35 and 40 peanut butter pies in a day? (b) What is the probability that the demand is greater than 50 pies a day? (c) What is the demand that has a 1% chance of being exceeded?

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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.