# Suppose That X Is Normally Distributed With A Mean

Suppose that x is normally distributed with a mean of 30 and a standard deviation of 3. What is P(27. 42 ? x ? 34. 08)?a) 0. 718b) 0. 413c) 0. 309d) 0. 305e) 0. 415f) 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 aboveQuestion 3Suppose that x is normally distributed with a mean of 50 and a standard deviation of 9. What is P(33. 53 ? x ? 70. 97)?a) 0. 495b) 0. 466c) 0. 490d) 0. 956e) 0. 471f) None of the aboveQuestion 4The length of time needed to complete a certain test is normally distributed with mean 24 minutes and standard deviation 11 minutes. Find the probability that it will take between 22 and 28 minutes to complete the test. a) 0. 5000b) 0. 4279c) 0. 1070d) 0. 7859e) 0. 2141f) None of the aboveQuestion 5The length of time needed to complete a certain test is normally distributed with mean 23 minutes and standard deviation 11 minutes. Find the probability that it will take more than 20 minutes to complete the test. a) 0. 6075b) 0. 5000c) 0. 6963d) 0. 3925e) 0. 3037f) None of the aboveQuestion 6Which of the following statements is not true?a) The sampling distribution of sample mean is approximately normal, mound-shaped, and symmetric for n > 30 or n = 30. b) The expected value of the sample mean, X, is always the same as the expected value of X, the distribution of the population from which the sample was taken. c) The sampling distribution of the sample mean, X, is always reasonably like the distribution of X, the distribution from which the sample is taken. d) The standard deviation of the sampling distribution X of sample mean = ?/?n where ? is the standard deviation of X. e) The larger the sample size, the better will be the normal approximation to the sampling distribution of sample mean. f) None of the aboveQuestion 7Suppose a random sample of 70 measurements is selected from a population with a mean of 35 and a variance of 300. Select the pair that is the mean and standard error of x. a) [35, 2. 571]b) [35, 2. 371]c) [35, 2. 071]d) [70, 2. 571]e) [35, 2. 271]f) None of the aboveQuestion 8A random sample of 1024 12-ounce cans of fruit nectar is drawn from among all cans produced in a run. Prior experience has shown that the distribution of the contents has a mean of 12 ounces and a standard deviation of 0. 12 ounce. What is the probability that the mean contents of the 1024 sample cans is less than 11. 994 ounces?a) 0. 085b) 0. 095c) 0. 055d) 0. 075e) 0. 065f) None of the aboveQuestion 9The World Health Organization’s (W. H. O. ) recommended daily minimum of calories is 2600 per individual. The average number of calories ingested per capita per day for the US is approximately 2460 with a standard deviation of 500. If we take a random sample of 64 individuals from the US, what is the probability that the sample mean exceeds the W. H. O. minimum?a) 0. 013b) 0. 010c) 0. 017d) 0. 009e) 0. 015f) None of the aboveQuestion 10Current research indicates that the distribution of the life expectancies of a certain protozoan is normal with a mean of 43 days and a standard deviation of 10. 1 days. Find the probability that a simple random sample of 36 protozoa will have a mean life expectancy of 48 or more days. a) 0. 0015b) 0. 6897c) 0. 9985d) 0. 0030e) 0. 2015f) None of the aboveQuestion 11What effect does increasing the sample size have on a distribution of sample means?a) It will not make any differenceb) It will have less variationc) It will have more variationQuestion 12Suppose that a random sample of size 25 is to be selected from a population with mean 44 and standard deviation 7. What is the approximate probability that X will be within 0. 5 of the population mean?a) 0. 7210b) 0. 0569c) 0. 4790d) 0. 2790e) 0. 5580f) None of the aboveQuestion 13Suppose that a random sample of size 25 is to be selected from a population with mean 44 and standard deviation 7. What is the approximate probability that X will be more than 0. 5 away from the population mean?a) 0. 2790b) 0. 0569c) 0. 4790d) 0. 7210e) 0. 5580f) None of the aboveQuestion 14Lloyd’s Cereal company packages cereal in 1 pound boxes (16 ounces). A sample of 36 boxes is selected at random from the production line every hour, and if the average weight is less than 15 ounces, the machine is adjusted to increase the amount of cereal dispensed. If the mean for 1 hour is 1 pound and the standard deviation is 0. 2 pound, what is the probability that the amount dispensed per box will have to be increased?a) 0. 0304b) 0. 3773c) 0. 9696d) 0. 0608e) 0. 2304f) None of the aboveQuestion 15In a large population, 82% of the households have cable tv. A simple random sample of 225 households is to be contacted and the sample proportion computed. What is the mean and standard deviation of the sampling distribution of the sample proportions?a) mean = 184. 50, standard deviation = 0. 0256b) mean = 0. 82, standard deviation = 0. 0007c) mean = 184. 50, standard deviation = 0. 0007d) mean = 0. 82, standard deviation = 0. 0256e) mean = 0. 82, standard deviation = 0. 5656f) None of the aboveQuestion 16In a large population, 65% of the households have cable tv. A simple random sample of 256 households is to be contacted and the sample proportion computed. What is the probability that the sampling distribution of sample porportions is less than 59%?a) 0. 1169b) 0. 0110c) 0. 9779d) 0. 8831e) 0. 0221f) None of the above