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An Introduction to Mathematical Statistics and Its Applications (6th Edition)
- Let X be a continuous random variable with mean μ and standard deviation σ. If X is transformed to Y = 2X + 3, what are the mean and standard deviation of Y?arrow_forwardIf X is a continuous random variable, what is the value of X that will be exceeded 30% of the time, ifX is uniformly distributed with a mean of 6 and a variance of 12?arrow_forwardAn analogue signal received at a detector, measured in microvolts, is normally distributed with mean of 185 and variance of 244. What is the probability that is the signal will be less than 203 µV given that it is less than 184 µV?arrow_forward
- The average number of pounds of sliced ham ordered per customer at the deli where Dennis used to work was 1.4, but at his new job, the average of the 32 people who have ordered ham so far is 1.5 pounds, with a standard deviation of 0.3 pounds. a) Write the null and alternative hypotheses to test if the average amount of ham bought is higher at the new store. H0:μ= H1:μ> b) For α=0.025, find the rejection region in terms of z. [Write your answer with 2 decimal places.] R:z≥ c) What test statistic corresponds to an x¯ of 1.5 pounds? [Round your answer to 2 decimal places.] z= d) Should you reject the null hypothesis?arrow_forwardThe teachers at a primary school have devised a particular method to teach arithmetic. They want to find out if this method produces dispersion in mean scores. In order to do so, at first, they took a sample of 25 students who were taught that particular method of arithmetic. Then their test scores were taken into consideration, assuming that the test scores of all the students in that school are approximately normally distributed. Their test score produced an average variance of 180 while the population is assumed to produce a test score of 165. Using a 95% confidence level, can you conclude that the variance of all the test scores of that primary school is different from 165?arrow_forwardSuppose that X1, . . . , Xn is a random sample from the Normal distribution N (0, σ2 ) with parameter σ > 0, Find the Maximum Likelihood Estimation of σ.arrow_forward
- A statistician claims that the standard deviation of the weights of firemen is more than 25 pounds. A sample of 20 randomly chosen firemen had a standard deviation of their weights of 26.2 pounds. Assume the variable is normally distributed. At alpha=0.05 what is the critical value χ2 for this test?arrow_forwardLet X1, X2, …, Xn be a random sample from the Normal distribution N() (a) Using method of moments to estimate the parameters and . (b) Are those estimators unbiased?arrow_forwardIf X is a continuous random variable, what is the value of X that will be exceeded 30% of the time, if 1. X is exponentially distributed with a variance of 1? 2. X has a chi-squared distribution with mean of 10?arrow_forward
- The number of ice creams sold per hour from Mr Fishy’s van is observed to be a Poisson random variable with parameter λ = 8. Each ice cream costs two pounds but Mr Fishy has to pay five pounds per hour for the pitch. What is the variance of his hourly profit (measured in pounds and ignoring all other income and expenses)?arrow_forwardThe daily demand for a certain product is approximately normally distributed with mean 50 and a variance of 125. If x is the daily demand for the product, what is the probability that x is exactly equal to 45?arrow_forwardThe daily demand for a certain product is approximately normally distributed with mean 50 and a variance of 100. If x is the daily demand for the product, what is the probability that x is greater than 50?arrow_forward
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