Suppose that we are attempting to locate a target in three-dimensional space, and that the three coordinate errors (in meters) of the point chosen are independent normal random variables with mean 0 and standard deviation 2. Find the probability that the distance between the point chosen and the target exceeds 3 meters.
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- Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The executives hire a statistical consultant and ask her to determine the mean shopping time, u, of customers at the supermarkets. The consultant will collect a random sample of shopping times at the supermarkets and use the mean of these shopping times to estimate u. Assuming that the standard deviation of the population of shopping times at the supermarkets is 27 minutes, what is the minimum sample size she must collect in order for her to be 99% confident that her estimate is within 5 minutes of u? Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements). (If necessary, consult a list of formulas.) ?To compare the dry braking distances from 30 to 0 miles per hour for two makes of automobiles, a safety engineer conducts braking tests for 35 models of Make A and 35 models of Make B. The mean braking distance for Make A is 43 feet. Assume the population standard deviation is 4.6 feet. The mean braking distance for Make B is 46 feet. Assume the population standard deviation is 4.5 feet. At α=0.10, can the engineer support the claim that the mean braking distances are different for the two makes of automobiles? Assume the samples are random and independent, and the populations are normally distributed. The critical value(s) is/are Find the standardized test statistic z for μ1−μ2.The Central Limit Theorem says that the standard deviation of the sampling distribution of the sample means is (A exactly equal to the standard deviation. (B close to the population mean if the sample size is small close to the population standard deviation if the sample size is large. equal to the population standard deviation divided by the square root of the sample D size.
- Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The executives hire a statistical consultant and ask her to determine the mean shopping time, μ, of customers at the supermarkets. The consultant will collect a random sample of shopping times at the supermarkets and use the mean of these shopping times to estimate μ. Assuming that the standard deviation of the population of shopping times at the supermarkets is 26 minutes, what is the minimum sample size she must collect in order for her to be 90%confident that her estimate is within 5 minutes of μ? Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements).Assume that females have pulse rates that are normally distributed with a mean of μ = 73.0 bpm and a standard deviation of σ = 12.5 beats per minute. A) If one adult female is randomly selected find the probability that her pulse rate is less than 80 bpm. B) if 25 adult females are randomly selected find the probability that they have pulse rates with a mean less than 80 bpmAn IQ test is designed so that the mean is 100 and the standard deviation is 14 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 90% confidence that the sample mean is within 2 IQ points of the true mean. Assume that σ=14 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.The required sample size is
- Use the central limit theorem to find the mean and standard error of the mean of the indicated sampling distribution. Then sketch a graph of the sampling distribution. The per capita consumption of red meat by people in a country in a recent year was normally distributed, with a mean of 113 pounds and a standard deviation of 37.7 pounds. Random samples of size 20 are drawn from this population and the mean of each sample is determined.Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The executives hire a statistical consultant and ask her to determine the mean shopping time, μ, of customers at the supermarkets. The consultant will collect a random sample of shopping times at the supermarkets and use the mean of these shopping times to estimate μ. Assuming that the standard deviation of the population of shopping times at the supermarkets is 27 minutes, what is the minimum sample size she must collect in order for her to be 95% confident that her estimate is within 5 minutes of μ? Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements).Assume that females have pulse rates that are normally distributed with a mean of μ=72.0 beats per minute and a standard deviation of σ=12.5 beats per minute. a) If 25 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 76 beats per minute.