Statistics and Probability Answers

A bag contains 6 white and 9 black balls . Four balls are drawn at a time .Find the probability for the first draw to give four white and second draw to give four black balls in each of the following cases:

a) The balls are replaced before the second draw.

b) The balls are not replaced before the second draw

Let X be the thickness of washers a machine turns out. Assume that x has the density f(x)=2.5x if 1.9 < x < 2.1 and 0 otherwish then calculate the probability that washer will have thickness between 1.95mm and 2.05 mm.

. From a box of a dozen rocket-propelled grenade (RPG), 4 are selected at random and fired. If the box contains 3 defective RPG’s, what is the probability that (a) all 4 will fire? (b) at most 2 will not fire?m

A secretary makes 2 errors per page, on average. What is the probability that on the next page she will make (a) 3 or more errors; (b) no errors?

Random samples of size 4 are drawn wigh replacement from a finite population 3,6,9. How many possible samples of size 4 are possible? Find the mean of the sample means.

Random samples of size 4 are drawn with replacement from a finite population 3,6,9. How many possible samples of size 4 are possible? Find the mean of the sample means

Solve the given problems.

1. A population consists of the four numbers 1, 2, 4 and 5. List all the possible

samples of size n = 3 which can be drawn with replacement from the population.

Find the following:

a. Population mean

b. Population variance

c. Population standard deviation.

d. Mean of the sampling distribution of sample means

e. Variance of the sampling distribution of sample means

f. Standard deviation of the sampling distribution of sample means

2. A population consists of the four numbers 1, 2, 8, and 9. List all the possible

samples of size n = 2 which can be drawn without replacement from the population. 

Find the following:

a. Population mean

b. Population variance

c. Population standard deviation

d. Mean of the sampling distribution of sample means

e. Variance of the sampling distribution of sample means

f. Standard deviation of the sampling distribution of sample means

Solve the given problems.

1. A population consists of the four numbers 1, 2, 4 and 5. List all the possible

samples of size n = 3 which can be drawn with replacement from the population.

Find the following:

a. Population mean

b. Population variance

c. Population standard deviation.

d. Mean of the sampling distribution of sample means

e. Variance of the sampling distribution of sample means

f. Standard deviation of the sampling distribution of sample means

Solve the following problems. Use the properties of the sampling distribution of

sample means.

5. If a population with size 3 has a standard deviation of 2.4, what is thestandard 

deviation of the sampling distribution of its means? The sampling distribution 

has a sample size of 2 and all possible samples are drawn without

replacements.

Solve the following problems. Use the properties of the sampling distribution of

sample means.

1. If a population has a mean of 5.7, what is the mean of the sampling distribution

of its means?

2. If a population has a variance of 7.4, what is the variance of the sampling

distribution of its means? The sampling distribution has a sample size of 2

and all possible samples are drawn with replacements.

3. If a population has a standard deviation of 3.2, what is the standard deviation

of the sampling distribution of its means? The sampling distribution has a

sample size of 4 and all possible samples are drawn with replacements.

4. If a population with size of 4 has a variance of 6.8, what is the variance of the

sampling distribution of its means? The sampling distribution has a sample size

of 3 and all possible samples are drawn without replacements.