A simple random sample of sizen is drawn from a population that is normally distributed. The sample mean, x, is found to be 110, and the sample standard deviation s, is found to be 10. (a) Construct an 80% confidence interval about u if the sample size, n, is 15. (b) Construct an 80% confidence interval about u if the sample size, n, is 28. (c) Construct a 90% confidence interval about u if the sample size, n, is 15. (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed? Click the icon to view the table of areas under the t-distribution. (a) Construct an 80% confidence interval about u if the sample size, n, is 15. Lower bound: 106.5 ; Upper bound: 113.5 (Use ascending order. Round to one decimal place as needed.) (b) Construct an 80% confidence interval about u if the sample size, n, is 28. Lower bound: ; Upper bound: (Use ascending order. Round to one decimal place as needed.)
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.
Please answer parts B, C and D.
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