**Sample Size Calculations and Confidence Intervals** **13. Basic Computation: Sample Size** Suppose \( x \) has a mound-shaped distribution with \( \sigma = 3 \). - (a) Find the minimal sample size required so that for a 95% confidence interval, the maximal margin of error is \( E = 0.4 \). - (b) Check Requirements: Based on this sample size, can we assume that the \( \bar{x} \) distribution is approximately normal? Explain. **14. Basic Computation: Sample Size** Suppose \( x \) has a normal distribution with \( \sigma = 1.2 \). - (a) Find the minimal sample size required so that for a 90% confidence interval, the maximal margin of error is \( E = 0.5 \). - (b) Check Requirements: Based on this sample size and the \( \bar{x} \) distribution, can we assume that the \( \bar{x} \) distribution is approximately normal? Explain. **15. Zoology: Hummingbirds** Allen’s hummingbird (*Selasphorus sasin*) has been studied by zoologist Bill Alther (Reference: *Hummingbirds* by K. Long and W. Alther). A small group of 15 Allen’s hummingbirds has been under study in Arizona. The average weight for these birds is \( \bar{x} = 3.15 \) grams. Based on previous studies, we can assume that the weights of Allen’s hummingbirds are normally distributed, with \( \sigma = 0.33 \) gram. - (a) Find an 80% confidence interval for the average weight of Allen’s hummingbirds in the study region. What is the margin of error? - (b) What conditions are necessary for your calculations? - (c) Interpret: Compare your results in the context of this problem. - (d) Sample Size: Find the sample size necessary for an 80% confidence level with a maximal margin of error \( E = 0.08 \) for the mean weight of the hummingbirds. **16. Diagnostic Tests: Uric Acid** Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advance indication of illness such as gout, leukemia, or lymphoma (Reference: *A Manual of Laboratory and Diagnostic Tests* by F. Fischbach).

Problem 4 (6.EE.A.3) Which expression is equivalent to 5(4x + 3)-2x? A. 18x+15 B. 18x +3 C 7x+8 D. 2x +8

The picture below shows a variant of a famous paradoxical puzzle. On the left, we take two rectanglesof area 60, and cut each one into two pieces. On the right, we rearrange the four pieces, and put themtogether into a single rectangle of area 119. How could this be? Thoroughly explain why this is wrong mathematically (don't just say there is a gap, use numerical equations and stuff). If you need help, search "chessboard paradox" or "missing square puzzle".

Multiplication Problem 6: Find A x B A = = B = 12 34 - 1 0 1 2

Solve the following problems: (b) A states license plate has 7 characters. Each character can be a capital letter (A - Z), or a non-zero digit (1 - 9). How many license plates start with 3 capital letters and end with 4 digits with no letter or digit repeated?

Answer please

Homework 10: Question 1

Problem. 5 : Perform the indicated operations. -2 1 214 -1 -1 -21 5 1 -2 -3 -1 1 1 1 -2 0 -2

Snape made a deposit of $495 into an account that pays 3% interest compounded annually. How much money is in the bank after 3 years?

(Mathematical Classic of Chang Ch'iu-chien: the Problem of the Hundred Fowls) If a cock is worth 5 coins, a hen 3 coins, and three chicks together 1 coin, how many cocks, hens, and chicks, totaling 100, can be bought for 100 coins?