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Problem 1:
A dataset contains information on travel behavior of male and female workers of a small office. A total of 50 workers drive (27 males and 23 females) and 30 others use transit (14 males and 16 females). If we randomly choose one individual,
a. What is the probability that the individual is a driver?
b. What is the probability that the individual is male?c. What is the probability that it is a male driver? d. What is the probability that it is a female or a transit user?If we randomly pick two individuals, e. What is the probability that both are transit users?
Problem 2:
A long-term record for weather in a certain province shows that the annual precipitation has a mean of 39.67 inches and a standard deviation of 4.38 inches. If the annual precipitation amount has a normal distribution, what is the probability that next year the total precipitation will be:
a. more than 50.0 inches?b. between 42.0 and 48.0 inches?c. between 30.0 and 37.5 inches?d. more than 35.0 inches?e. less than 45.0 inches?f. less than 32.0 inches?
A population consists of 15 items, 10 of which are acceptable. In a sample of 4 items, what is the probability that exactly 3 are acceptable? Assume the samples are drawn without replacement.
Select 3 differently shaped flowers from a florist or grocery store - (Walmart even has a decent selection - a lily, a carnation, and a snapdragon are all nice and very different from one another).
The thickness of a flange on an aircraft component is uniformly distributed between 0.95 and 1.05 millimeters. Determine the cumulative distribution function of flange thickness.
In a sample of 80 mail carriers 16 had been bitten. At the 0.05 level of confidence, is there a significant difference in the proportions?
Which of the following would produce a new confidence interval with smaller width based on these same data and produce a new confidence interval
A sample of 121 provided a sample mean of 77.3. The population standard deviation is known to be 16.5. Compute the value of the test statistic.
One sample has a variance of s2=6 and a second sample has a variance of s2=8. If the two samples are the same size (n1=n2), then what is the pooled variance for the two samples?
The F-test cannot be used to answer whether or not there is a significant difference between the means.
How is the MLE and the Wald statistic distributed? For confidence intervals and hypothesis tests. How is the likelihood ratio statistic distributed?
Let X 1 , X 2 , ... , X n be a random sample from the distribution with probability density function f(x; Θ) = [Θ / 2sqrt(x)] * e^[-Θsqrt(x)], x > 0 , Θ > 0. What is the probability distribution of sigma notation from i = 1 to n (sqrt(Xi))?
Cite an example of your experience with applying Six Sigma tools for Statistical significance in the workplace. If you do not have an actual example, suggest a situation or context in which the tools would provide valuable quality improvement help..
The combined SAT scores of students are normall distributed with a mean of 950 and a standard deviation of 200. What are the minimum and the mximum values of the middle 87.4% of the scores.
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