### 7.22 Because \( P(z < 0.44) = 0.67 \), 67% of all \( z \) values are less than 0.44, and 0.44 is the 67th percentile of the standard normal distribution. Determine the value of each of the following percentiles for the standard normal distribution (Hint: If the cumulative area that you must look for does not appear in the \( z \) table, use the closest entry): a. The 91st percentile (Hint: Look for area 0.9100.) b. The 77th percentile c. The 50th percentile d. The 9th percentile e. What is the relationship between the 70th \( z \) percentile and the 30th \( z \) percentile?

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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.