1 Suppose a random sample of 50 measurements is selected fro

1. Suppose a random sample of 50 measurements is selected from a population with a mean of 55 and a variance of 400. Select the pair that is the mean and standard error of x.

2.A random sample of 625 10-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 10 ounces and a standard deviation of .10 ounce. What is the probability that the mean contents of the 625 sample cans is less than 9.995 ounces?

3.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 36 individuals from the US, what is the probability that the sample mean exceeds the W.H.O. minimum?

4.Current research indicates that the distribution of the life expectancies of a certain protozoan is normal with a mean of 49 days and a standard deviation of 10.5 days. Find the probability that a simple random sample of 49 protozoa will have a mean life expectancy of 50 or more days.

5.Suppose that a random sample of size 49 is to be selected from a population with mean 49 and standard deviation 6. What is the approximate probability that X will be within .5 of the population mean?

6.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 more than .5 away from the population mean?

7.Lloyd\'s Cereal company packages cereal in 1 pound boxes (16 ounces). A sample of 25 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?

8.The gas mileage for a certain model of car is known to have a standard deviation of 4 mi/gallon. A simple random sample of 16 cars of this model is chosen and found to have a mean gas mileage of 27.5 mi/gallon. Give the interval that would include the middle 95% for the sampling distribution of the mean gas mileage for this car model.

Solution

Note we are suppose to answer 1 question at a time, i will give u solution of 1st for rest repost again.

1)Standard error of mean = Standard deviation/sqrt n
Standard deviation = sqrt variance = sqrt 400 = 20
S.E of mean = 20 / sqrt 50 = 2.82
therefore Mean and standard error are (55 , 2.82)