A recent study at a local university found that the average number of words a two-year old knows is normally distributed with a mean of 116 words and a standard deviation of about 52 words. Assume that forty-nine two-year olds are randomly chosen and a test is given to determine the number of words that they currently know. Answer the following questions. Round all answers to 4 decimal places. a. What is the distribution of ? a - N( 116 b. In a group of 49 two-year olds, find the probability that the average number of words known is more 7.4286 than 106. c. Find the third quartile for the average number of words a two-year old knows. d. For part b), is the assumption that the distribution is normal necessary? O YesO No

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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.