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Suppose that births are equally likely to be on any day. What is the probability that somebody chosen at random has a ba birthday on the first day of a month? How does this probability change condi
A dreidel is a four-sided top that contains a Hebrew letter on each side: nun, gimmel, heh, shin. Here we suppose that a fair dreidel is to be spun ten times. Compute the probability of each of the
Suppose we roll three fair six-sided dice. Compute the conditional probability that the first die shows 4, given that the sum of the three numbers showing is 12.
Suppose Alice flips three fair coins, and let X be the number of heads showing. Suppose Barbara flips five fair coins, and let Y be the number of heads showing. Let Z =X -Y . Compute P(Z= z) for eve
Calculate the density and its 95 percent confidence limit of error, and present it and its limit of error in proper form with the correct number of significant figures and proper units.
Calculate the number (n) of moles of HCl in the solution dispensed. Give S and Sm for the initial and final volumes, and give a limit of error (95 percent confidence) for n.
A person leaves for work between 8 am and 8.30 am and takes between 40 and 50 minutes to get there. Let the random variable X denote her time of departure and the random variable Y the travel time.
A state administered standardized reading exam is given to eighth grade students. The scores on this exam for all students statewide have a normal distribution with a mean of 536 and a standard devi
A random sample of 15 student nurses were given a test to measure their level of "authoritarianism" with the following ordinal-scale results. Test the null hypothesis that the typical (median) score
A bagel shop wants to estimate their daily demand for their popular poppy seed bagel. The shop owner determined that the daily demand follows the normal probability model with mean 300 bagels and st
How many samples of 5 contain exactly one nonconforming chip? How many samples of 5 contain at least one nonconforming chip?
Five percent of computer parts produced by a certain supplier are defective. What is the probability that a sample of 16 parts contains more than 3 defective ones?
In a pizzeria they offer eight different toppings for a pizza. Moreover you are allowed to double any topping if you wish. For example, it is possible to get a pizza with: single type 1 topping, do
How many 3-digit numbers have distinct non-zero digits? Generalize your answer for a k-digit number, where k =< 9.
An interactive system consists of ten terminals that are connected to the central com- puter. At any time, each terminal is ready to transmit a message with probability 0.7, independently of other t
You play a dice game with two dice. If you roll at most 5 (i.e. the sum of the two numbers is 2, 3, 4 or 5) then you win, if you roll 7 or 10 then you lose, otherwise you have to roll again. What i
A 95% confidence interval for a population mean, u, is given as (18.958, 21.015). This confidence interval is based on a simple random sample of 36 observations. Calculate the sample mean, standard
Compute expectations and variances of the total dollar profit generated by portfolios (a), (b), and (c). What is the least risky portfolio? What is the most risky portfolio?
Raid 1 scheme splits the data over two hard drives. What is the probability of data loss? Assume that the data loss occurs if at least one drive fails within the same day.
Furthermore, an analysis of heart attack victims reveals that 12% of low-income people, 9% of medium-income people, and 7% of high-income people die of heart attacks. Find the probability that a sur
The magement of a manufacturing plant is studying the number of times employees in a large population of workers are absent. A random sample of 25 employees is chosen, and the average number of annu
You are interviewing a candidate who has failed the test, 0but you decide to hire the candidate anyway. What is the probability that this person will be with the company 1 year from now?
A batch of 50 different automatic typewriters contains exactly 10 defective machines. What is the probability of finding: