Consider the birthdays of the students in a class of size r. Assume that the year consists of 365 days. a. How many different ordered samples of birthdays are possible (r in sample) allowing repetitions (with replacement)?
b. The same as part (a), except requiring that all the students have different birthdays (without replacement)?
c. If we can assume that each ordered outcome in part (a) has the same probability, what is the probability that at least two students have the same birthday?
d. For what value of r is the probability in part (c) about equal to 1/2? Is this number surprisingly small? Hint: Use a calculator or computer to find r.

25 ! what is the value of x? enter your answer in the box. x =

Explain how to convert measurements in the metric system

In this problem, we explore the effect on the standard deviation of multiplying each data value in a data set by the same constant. consider the data set 14, 6, 8, 15, 15. (a) use the defining formula, the computation formula, or a calculator to compute s. (round your answer to one decimal place.) s = 4.28 (b) multiply each data value by 3 to obtain the new data set 42, 18, 24, 45, 45. compute s. (round your answer to one decimal place.) s = 12.83 (c) compare the results of parts (a) and (b). in general, how does the standard deviation change if each data value is multiplied by a constant c? multiplying each data value by the same constant c results in the standard deviation remaining the same. multiplying each data value by the same constant c results in the standard deviation being |c| times as large. multiplying each data value by the same constant c results in the standard deviation increasing by c units. multiplying each data value by the same constant c results in the standard deviation being |c| times smaller. (d) you recorded the weekly distances you bicycled in miles and computed the standard deviation to be s = 3.8 miles. your friend wants to know the standard deviation in kilometers. do you need to redo all the calculations? yes no given 1 mile ≠1.6 kilometers, what is the standard deviation in kilometers? (enter your answer to two decimal places.)