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The weight of eggs produced by u certain type of hen varies according to a distribution that is approximately normal with mean 6'5 grams and standard deviation 5 grams.
(a) What is the probability that a randomly selected from such a hen weighs more than 11.5 grams
(b) What is the probability that the average of a random sample of 25 eggs from such hens will be less than 5.8 grams ?
A professor is targeting a score of 80 on an exam. His forty-nine students averaged 78 on an exam with s = 7. Are the scores significantly less than 80 at a significance level of 0.05? Show your work and state the conclusion.
joint pmf p(X1,X2)=(X1+2X2)/18, (x1,x2)=(1,1),(1,2),(2,1),(2,2), zero elsewhere. Determine the conditional mean and variance of X2, given X1=x1, for x1=1 or 2. Also compute E(3X1-2X2).
"If you took 40 employees at random from the corporation, there is a pretty good chance the average number of days absent would be 12 or more. That's what happened to us-chance variation." Is this a good defense? Justify your answer.
After computing a confidence interval, the investigator believes that the results are meaningless because the width of the interval is too large. In reconstructing the interval, the investigator should: decrease the sample size.
Now assume that θ2 > 0 (with probability 1), and let δ1 hat be the Bayes estimator of 1/θ2 under the setup above. Show that δ1δ2 hat is the bayes estimator of θ1/θ2 , given x = (X1, X2).
A promotion campaign is being planned to encourage people to reduce heat in their houses at night. In order to measure the campaign's impact, we want to determine the proportion of people who reduce their heat at night.
What is the probability that a randomly selected cell phone bill is more than $67.75?
Top management earn between $50,000 and $100,000 per year. A histogram of all salaries would have which of the following shapes?
Exam is given to 20 randomly chosen students and their average length of t time needed to finish exam was 54 minutes with standard deviation of 5.99 minutes. Test instructor's claim at the 0.05 level of significance.
Suppose it is desired to estimate the population mean number of miles with a margin of error of ± 2 miles at 95% confidence. Do the data provide this desired level of precision? What action, if any, would you recommend be taken?
a. Define variables that would tell how many units to purchase from each source. b. Develop an objective function that would minimize the total cost.
In a one-way ANOVA analysis of 3 treatments, with the total number of 9 observations, with an equal number of observations in each treatment, mean-square-error (MSE) was found to be 24.905.
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