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prove that the sum of two algebraic integer is an algebraic integer
Let R = {(0,1),(0,2),(1,1,),(1,3),(2,2),(3,0)} be a relation defined on
A = {0,1,2,3}.Find the zero-one matrix of transitive closure of R.
1. Consider the set of even single-digit numbers {0, 2, 4, 6, 8}.
a. Make a list of possible sample size of 2 that can be taken from this sets of numbers.
b. Construct the sampling distribution of the sample means for the size of 3 and the standard variation.
2. In the numbers {1, 3, 5, 7, 9} construct the following:
a. List of possible sample size of 3 that can be taken from this sets of numbers.
b. Sampling distribution of the sample means for the size of 3 and the standard variation.
3. 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.
a. Find the mean of the sampling distribution.
b. Find the standard variation of the sampling distribution.
c. What is the probability that this sample mean will be between 40 and 50?
1. The height of grade 1 pupils is approximately normally distributed with µ = 45 inches and s = 2.
a. If an individual pupil is selected at random, what is the probability that he or she has a height of 42 and 47?
b. 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?
c. If a pupil is selected at random, what is the probability that is taller than 46 inches?
d. A class of 30 of these pupils is used as sample. What is the probability that the class mean is greater than 46 inches?
1. The height of grade 1 pupils is approximately normally distributed with µ = 45 inches and s = 2.
1. If an individual pupil is selected at random, what is the probability that he or she has a height of 42 and 47?
Prove that there is a positive multiple of 3333 which is entirely made of 0s and 1s. (For example: 110000011; note that we don’t need to find the number. We just need to prove that there exists such a number)
There are 150 students in a class. The distribution if their marks in a mathematics test are as follows
Class frequency
0-9 3
10-19 10
20-29 17
30-39 x
40-49 35
50-59 y
60-69 18
70-79 10
80-89 5
90-99 2
Required
i) The value of x given that the median mark is 44.357 (2marks)
ii) The value of y given that the modal is 43.0 (2marks)
iii) Draw an ogive of the data in (a) above (3 marks)
A box ha 3 netball and 6 volleyball card. What is the probability of selecting ....
A. A netball card, keeping it out, and then selecting another netball card?
B. A netball card, keeping it out, and then selecting another volleyball card?
A die is thrown 5 times. What is the probability of obtaining a 4 or 5?
A. Zero
B. Once
C. Twice
Hint: Calculate the p(4 or 5) for a single throw
irections. From your family members, form a group of five. (Just in case your
family is composed of less than five members, you can add one from your
neighbors). Get the weight in the kilogram of each member of the group. Draw
random samples of size 𝑛 = 2 from these weights.
1. List all possible samples and compute the mean of each sample.
2. Construct the sampling distribution of the sample means.
3. Find the mean of the population 𝜇.
4. Find the standard deviation of the population 𝜎.
5. Find the mean of the sampling distribution of the sample means 𝜇𝑋̅.
6. Find the standard deviation of the sampling distribution of the sample
means 𝜎𝑋̅.
7. Verify the Central Limit Theorem by:
a. Comparing 𝜇 and 𝜇𝑋̅.
b. Comparing 𝜎 and 𝜎𝑋̅.
