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If we experience an economic decline in the year 2008, what is the probability that there will a Republican president (to 4 decimals)?
Compute the probability that a person in the United States is age 65 or older. Given a person uses five or more prescriptions, compute the probability that the person is age 65 or older.
A distribution has a standard deviation of o = 12. Find the z-score for each of the following locations in the distributions.
Find the covariance between hourly wage X and education Y (measured in years of schooling) using the following summary statistics for a sample of 10 workers in a plant.
A university's leadership council is made up of members: are students, are teachers, and are deans. A newspaper reporter is planning to select two of the council members for interviews. The first me
The following data are from an experiment comparing three different treatment conditions.
The average male drinks 2L of water when active outdoors (with a standard deviation of 0.7L). You are planning a full day nature trip for 50 men and will bring 110L of water. What is the probability
An instructor who taught two sections of engineering statistics last term, the first with 20 students and the second with 40, decided to assign a term project. After all projects had been turned in,
What percent of respondents were under 30 and did not snore? Hint: Draw a Venn diagram to represent the region of interest.
A score of 75 or greater is needed to obtain an A on the exam. What percentage of the students received an A?
Define one and two dimensional random variables (discrete and continuous) with suitable examples. State the probability functions, cumulative probability functions, probability distributions of each
Given that an adult takes prescription drugs regularly, what is the probability that the adult is 65 or older?
Someone claims that the waiting time, in minutes, between hits at a certain website has an exponential distribution with parameter value of 1.
An automobile manufacturer gives a 5-year/60000 mile warranty on its drive train. Historically, 7% of this manufacturer's automobiles have required service under this warranty. Consider a random sam
A running track is 1 mile long. Two runners start on it at the same time. The speed of Runner i is Xi, i = 1 and 2. Suppose Xi ~ exp(λi), i = 1, 2, and X1 and X2 are independent. The mean spe
A manufacturer of water filters for refrigerators monitors the process for defective filters. Historically, this process averages 5% defective filters. Suppose five filters are selected for testing.
In one elementary school, 200 students are tested on the subject of math and english. The math mean is 67 with a standard deviation of 9.58 and the english mean is 78 with a SD of 12.45.
An urn is picked randomly (with probability 1/2 for each urn), and then a ball is uniformly drawn from that urn. Let A be the event that the ball drawn is white and let B be the event that the urn p
Five cards are independently and randomly picked from a standard 52 card deck and each card is recorded in sequence. Each card that is picked is then put back in the deck, so it is possible to recor
In the first quarter of a year, a company's records showed that 68% of its employees missed no work, 22% missed exactly one day of work, 8% missed exactly two days, and 2% missed exactly three days.
In the casino dice game of craps, the shooter rolls two (fair) dice. The shooter a) wins on the first roll if the sum of the dice is 7 or 11 and b) loses on the first roll if the dice total 2, 3, or
Let F hat denote the empirical distribution function based on a random sample X1,....Xn with common cdf F.= Show that E[ F hat (x)] = F(x) and Var[ F hat (x)] = F(x)(1 - F(x))=n.
Suppose that the we have the following data which comes from a distribution with probability density function
As an example consider an experiment with two outcomes, H & T. The first sample space has two points and each has a probability of p(T) and p(H). Suppose we repeat the process twice, two experim
Show that the ratio of two independent standard normal random variables has the t1 distribution.