Current research indicates that the distribution of the life expectancies of a certain protozoan is normal with a mean of 48 days and a standard deviation of 10.1 days. Find the probability that a simple random sample of 25 protozoa will have a mean life expectancy of 50 or more days. What effect does decreasing the sample size have on a distribution of sample means? In a large population, 74% of the households have cable tv. A simple random sample of 144 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? In a large population, 83% of the households have cable tv. A simple random sample of 121 households is to be contacted and the sample proportion computed. What is the probability that the sampling distribution of sample porportions is less than 75%? Which of the following statements is not true? a) The sampling distribution of the sample mean is always reasonably like the distribution of X, the distribution from which the sample is taken. b) The mean of the sampling distribution of sample mean is always the same as that of X, the distribution from which the sample is taken. c) The sampling distribution of sample mean is approximately normal, mound-shaped, and symmetric for n > 30 or n = 30. d) The standard deviation of the sampling distribution of sample mean = /n e) The larger the sample size, the better will be the normal approximation to the sampling distribution of sample mean. f) None of the above Suppose a random sample of 70 measurements is selected from a population with a mean of 65 and a variance of 300. Select the pair that is the mean and standard error of x. A 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 .12 ounce. What is the probability that the mean contents of the 1024 sample cans is less than 11.994 ounces? The 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 81 individuals from the US, what is the probability that the sample mean exceeds the W.H.O. minimum? Suppose that a random sample of size 36 is to be selected from a population with mean 43 and standard deviation 6. What is the approximate probability that X will be within .5 of the population mean? Suppose that a random sample of size 36 is to be selected from a population with mean 47 and standard deviation 8. What is the approximate probability that X will be more than .5 away from the population mean? Lloyd'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 0.1 pound, what is the probability that the amount dispensed per box will have to be increased? The gas mileage for a certain model of car is known to have a standard deviation of 5 mi/gallon. A simple random sample of 36 cars of this model is chosen and found to have a mean gas mileage of 25.6 mi/gallon. Give the interval that would include the middle 95% for the sampling distribution of the mean gas mileage for this car model. The weight of a randomly selected bag of corn chips coming off an assembly line is a random variable with mean =13 oz. and standard deviation =0.4 oz. Suppose we pick four bags at random assume that weight of each of the bags are independent. The combined weight of these four bags is a random variable with a mean of The weight of a randomly selected bag of corn chips coming off an assembly line is a random variable with mean =12 oz. and standard deviation =0.4 oz. Suppose we pick five bags at random assume that weight of each of the bags are independent. The combined weight of these five bags is a random variable with a standard deviation (in oz.) of The weight of a randomly selected bag of corn chips coming off an assembly line is a random variable with mean =12 oz. and standard deviation =0.3 oz. The weight of a randomly selected bag of corn chips in pounds (1 pound = 16 oz.) is a random variable with standard deviation The weight of a randomly selected bag of corn chips coming off an assembly line is a random variable with mean =10 oz. and standard deviation =0.3 oz. 4. Suppose we pick two bags at random from the assembly line. The difference in the weights of the two bags selected (the weight of the first bag minus the weight of the second bag) is a random variable with a mean (in oz.) of