Statistics and Probability Answers

Find the class boundaries, midpoints, and size for each class.

(a)  32 – 38

(b)  86 – 104

(c)  895 – 905

(d)  12.3 – 13.5

(e)  3.18 – 4.96 

How many ways can 4 baseball players and 3 basketball players be selected from 12 baseball players and 9 basketball players?

The heights of the population of boys are normally distributed with a mean of 66 inches and al standard deviation of 8.9 inches. If a random sample of 40 boys is drawn from this population, what is the probability that the mean of this sample is greater than 64.5 inches?

A sample size of 36 is to be selected from a population that has a mean of µ = 45 and standard deviation s of 10.

• Find the mean of the sampling distribution
• Find the standard error of the sampling distribution.
• What is the probability that this sample mean will be between 40 and 50?

The height of grade 1 pupils are approximately normally distributed with µ = 45 inches and s = 2.

• If an individual pupil is selected at random, what is the probability that he or she has a height of 42 and 47?
• A class of 30 of these pupils is used as a sample. What is the probability that the class mean is between 42 and 47?
• If a pupil is selected at random, what is the probability that is taller than 46 inches?
• A class of 30 of these pupils is used as sample. What is the probability that the class mean is greater than 46 inches?

14. The number of absences from June to March of a student based on

his class adviser's record is shown below.

Month No. of Absences Month No. of Absences

June

November

2

July

2

December

1

August

1

January

4

September

3

February

1

October

March

If X be the random variable representing the number of absences. Which

table represents the probability distribution?

A.

1

2

3

P(X)

2/10

2/10

3/10

3/10

В.

1

2

3/10

3

3/10

PX)

1/10

3/10

C.

1

3

4

X

P(X)

O

1/10

2

3/10

1/10

3/10

1/5

X

O

1

2

3

PX)

1/5

3/10

3/ 10

1/10

1/10

Suppose X and Y are jointly normal random variables. Briefly discuss bivariate Normal distribution. Your answer should include, but not limited to, the joint pdf of the bivariate normal distribution f(x, y), it's properties including, but not limited to, E(Y/X=x) and V(Y/X=x).

Discrete random variables

A population consists of the numbers 5, 7, 9,

11, 12, and 15. List all possible sample size of

2 from this population and give the following:

•A. Determine the number of sets of all possible random samples that

can be drawn from the given population.

• B. List all possible samples and compute the mean of each sample.

• C. Construct the sampling distribution.

•D. Construct a histogram of the sampling distribution of the means.

two balls are drawn in succession without replacement from a jar containing 7 red balls and 6 blue balls. Let B be the random variable representing the number of blue balls. Find the mean.