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- Suppose that a very large number of random samples of size 25 are selected from a population with mean u and standard deviation o. If the mean of all the X's found is 300 and the standard deviation of these X's is 20, what are the estimates of the true mean and the true standard deviation or of the distribution from which the samples were drawnLet Xi be the allowance the boy gets in the ith week. Assuming a year has 52 weeks, what are the expected vaule, variance, and standard deviation of the total amount of allowance that the boy can get in a year X1+X2+X3...X52?2. Suppose that at a gas station the daily demand for regular gasoline is normally distributed with a mean of 1000 gallons and a standard deviation of 100 gallons. The station manager has just opened the station for business and there is exactly 2300 gallons of regular gasoline in storage. The next delivery is scheduled later tomorrow at the close of business. (a) Let X1 and X2 denote the demand of today and tomorrow, respectively. Let X = X1 + X2. Find the distribution of X. (b) Find the probability that the manager will have enough regular gasoline to satisfy today’s and tomorrow’s demand.
- A sample of 2000 observations has a mean of 74 and a standard deviation of 12. Using Chebyshev’s theorem, find the minimum percentage of the observations that fall in the intervals x +/- 2s, x +/- 2.5s and x +/- 3s Note that x +/- 2s represents the interval x - 2s to x + 2s, and so on Also note that s is symbol for standard deviation in this exampleA certain population has a mean of 200 and standard deviation of 50. If all random samples of size 100 are drawn from this population, the resulting distribution of X will have a mean of _________.A sample from a population witha mean of μ = 40, and a standard deviation of σ = 10, has a mean of x̅ = 44. If the sample mean corresponds to a z-score of z = +2.00, then how many scores are in the sample?
- Show that if X is a discrete random variable a mean of mu and a standard deviation sigma, then Z=(X-mu)/sigma is a discrete random variable with a mean of zero and a standard deviation of 11) Suppose that 1,000 students took a Math examination wherein the maximum score that they can obtain is 100. Thea average score is 70 with a standard deviation of 5. How many of the students obtained a score from 70 to 95?Chebyshev's Theorem states that for any set of numbers, the fraction that will like within k Standard deviations of the mean is at least 1- 1/k2. Use this theorem to find the fraxtion of all the numbers of a data that must lie within 3 standard deviations from the mean.
- Let x1, x2, and x3 be a random sample from and exponential distribution with mean θ. Suppose that θhat = (x1+x2)/2 is an estimator of θ. 1. Find out if the estimator is biased or unbiased. [Show your solution.] 2. Compute for the variance of the given estimator.9% of a population has a disease. 800 are randomly selected . What is the mean of people with the disease in such groups of 800 rounded to the third decimal place?1i. Suppose that a structure can withstand a flood with a peak discharge no greater than 1,950 m3/s and it has been designed to have an economic life span of 100 years. Determine the risk of failure assuming the Extreme Value Distribution when the mean and standard deviation of the annual flood series are 410m3/s and 280 m3/s, respectively. 1ii. What is the probability that at least one flood of ARI 50y (T=50y) will occur during the 30 year design life of a flood control project? 1iii. Consider a small, temporary (3 year design life) flood mitigation dam designed to contain a 20 year flood event. What is the risk that it will be overtopped at least once in the design life.
