# Math 2311-Suppose That X Is Normally Distributed With

Suppose that x is normally distributed with a mean of 20 and astandard deviation of 6. What is P(13. 82 ? x ? 29. 18)?a) 0. 351b) 0. 437c) 0. 785d) 0. 440e) 0. 348f) None of the aboveQuestion 2Find a value of c so that P(Z ? c) = 0. 48. a) 0. 95b) 0. 05c) 0. 15d) 0. 05e) 0. 10f) None of the aboveReview LaterReview LaterQuestion 3Suppose that x is normally distributed with a mean of 20 and astandard deviation of 6. What is P(13. 82 ? x ? 29. 18)?a) 0. 351b) 0. 437c) 0. 785d) 0. 440e) 0. 348f) None of the aboveReview LaterQuestion 4The length of time needed to complete a certain test is normallydistributed with mean 74 minutes and standard deviation 12minutes. Find the probability that it will take between 72 and 77minutes to complete the test. a) 0. 0824b) 0. 1649c) 0. 4338d) 0. 8351e) 0. 5000f) None of the aboveReview LaterQuestion 5The length of time needed to complete a certain test is normallydistributed with mean 31 minutes and standard deviation 6minutes. Find the probability that it will take more than 35 minutesto complete the test. a) 0. 1262b) 0. 2525c) 0. 8738d) 0. 7475e) 0. 5000f) None of the aboveReview LaterQuestion 6Which of the following statements is not true?a) The sampling distribution of the sample mean, X, is alwaysreasonably like the distribution of X, the distribution from whichthe sample is taken. b) The larger the sample size, the better will be the normalapproximation to the sampling distribution of sample mean. c) The standard deviation of the sampling distribution X of samplemean = ?/?n where ? is the standard deviation of X. d) The sampling distribution of sample mean is approximatelynormal, moundshaped, and symmetric for n >, 30 or n = 30. e) The expected value of the sample mean, X, is always the sameas the expected value of X, the distribution of the population fromwhich the sample was taken. f) None of the aboveReview LaterQuestion 7Suppose a random sample of 60 measurements is selected from apopulation with a mean of 25 and a variance of 200. Select the pairthat is the mean and standard error of x. a) [25, 1. 825]b) [25, 1. 925]c) [60, 2. 325]d) [25, 2. 225]e) [25, 2. 325]f) None of the aboveReview LaterQuestion 8A random sample of 784 10ounce cans of fruit nectar is drawnfrom among all cans produced in a run. Prior experience has shownthat the distribution of the contents has a mean of 10 ounces and astandard deviation of 0. 10 ounce. What is the probability that themean contents of the 784 sample cans is less than 9. 995 ounces?a) 0. 111b) 0. 081c) 0. 131d) 0. 121e) 0. 101f) None of the aboveReview LaterQuestion 9The World Health Organization’s (W. H. O. ) recommended dailyminimum of calories is 2600 per individual. The average numberof calories ingested per capita per day for the US is approximately2460 with a standard deviation of 500. If we take a random sampleof 81 individuals from the US, what is the probability that thesample mean exceeds the W. H. O. minimum?a) 0. 006b) 0. 007c) 0. 004d) 0. 003e) 0. 005f) None of the aboveReview LaterQuestion 10Current research indicates that the distribution of the lifeexpectancies of a certain protozoan is normal with a mean of 43days and a standard deviation of 10. 5 days. Find the probabilitythat a simple random sample of 64 protozoa will have a mean lifeexpectancy of 46 or more days. a) 0. 2111b) 0. 9889c) 0. 6125d) 0. 0111e) 0. 0223f) None of the aboveReview LaterQuestion 11Whateffect does decreasing the sample size have on a distributionof sample means?a) It will have more variationb) It will not make any differencec) It will have less variationReview LaterQuestion 12Suppose that a random sample of size 36 is to be selected from apopulation with mean 43 and standard deviation 6. What is theapproximate probability that X will be within 0. 5 of the populationmean?a) 0. 7658b) 0. 3829c) 0. 5829d) 0. 0664e) 0. 6171f) None of the aboveReview LaterQuestion 13Suppose that a random sample of size 49 is to be selected from apopulation with mean 49 and standard deviation 6. What is theapproximate probability that X will be more than 0. 5 away fromthe population mean?a) 0. 4403b) 0. 6403c) 0. 8807d) 0. 0664e) 0. 5597f) None of the aboveReview LaterQuestion 14Lloyd’s Cereal company packages cereal in 1 pound boxes (16ounces). A sample of 64 boxes is selected at random from theproduction line every hour, and if the average weight is less than15 ounces, the machine is adjusted to increase the amount of cerealdispensed. If the mean for 1 hour is 1 pound and the standarddeviation is 0. 2 pound, what is the probability that the amountdispensed per box will have to be increased?a) 0. 0124b) 0. 3773c) 0. 2062d) 0. 9938e) 0. 0062f) None of the aboveReview LaterQuestion 15In a large population, 67% of the households have cable tv. Asimple random sample of 256 households is to be contacted andthe sample proportion computed. What is the mean and standarddeviation of the sampling distribution of the sample proportions?a) mean = 171. 52, standard deviation = 0. 0009b) mean = 0. 67, standard deviation = 0. 6694c) mean = 0. 67, standard deviation = 0. 0294d) mean = 0. 67, standard deviation = 0. 0009e) mean = 171. 52, standard deviation = 0. 0294f) None of the aboveReview LaterQuestion 16In a large population, 67% of the households have cable tv. Asimple random sample of 256 households is to be contacted andthe sample proportion computed. What is the probability that thesampling distribution of sample porportions is less than 73%?a) 0. 0206b) 0. 4897c) 0. 9794d) 0. 8796e) 0. 1204f) None of the above