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(a) A student who waits for two buses every day records the status of the arrival of each bus. The bus is either late, on time, or early. The outcome of interest is the status of each bus for one day.
(b) Two standard decks of cards (consisting of 13 hearts, 13 diamonds, 13 spades and 13 clubs) is shuffled. One card from each deck is picked. The outcome of interest is the suit that is selected from each deck.
Cars arrive at a toll booth at a mean rate of five cars every 10 minutes according to a Poisson process. Find the probability that the toll collector will have to wait longer than 26.30 minutes before collecting the eighth toll.
A sample of 140 golfers showed that their average score on a particular golf course was 93.38 with a standard deviation of 4.36. Answer each of the following (show all work and state the final answer to at least two decimal places.):
A certain type of light bulb that is used on a projector has a Weibull distribution with parameters α=2, and β=3. Compute the following: The probability that the bulb will last 6.
a) 95% of confidence intervals generated will include the sample mean X. b) 5% of the confidence intervals generated will include the true mean μ
Units with weights less than 5.8 or greater than 6.2 ounces will be classified as defects. What is the probability of a defect (to 4 decimals)?
If "fair" coin is tossed four times and comes up heads all four times, probability of heads on the fifth trial is?
The following data were collected as part of a study of coffee consumption among male and female undergraduate students. The following reflects cups per day consumed:
How large could a tumor grow before a researcher might consider it to be an outlier and would want to double check the measurement.
The acceptance rate for applicants with similar qualifications is 30% for University X and 55% for University Y. What is the probability that Jim will be accepted by at least one of the two universities?
What is the expected number of patients arriving each Saturday and what is the most probable number of patients arriving each Saturday?
Suppose the time interval between two consecutive defective light bulbs from a production line has a uniform distribution over an interval from 0 to 90 minutes.
How to prove the natural parameter space of an exponential model is convex without using Holders inequality and other complex theories?
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