len's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.t Suppose a small group of 13 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is x= 3.15 grams. Based on previous studies, we an assume that the weights of Allen's hummingbirds have a normal distribution, with o = 0.24 gram. a) Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. What is the margin of error? (Round your answers to two decimal places.) lower limit upper limit margin of error b) What conditions are necessary for your calculations? (Select all that apply.) O n is large O uniform distribution of weights O a is unknown O normal distribution of weights O a is known c) Interpret your results in the context of this problem. O The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80. O We are 20% confident that the true average weight Allen's hummingbirds falls within this interval. O we are 80% confident that the true average weight of Allen's hummingbirds falls within this interval. O The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20. d) Find the sample size necessary for an 80% confidence level with maximal margin of error E = 0.10 for the mean weights of the hummingbirds. (Round up to the nearest whole number.) hummingbirds

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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.