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**Assignment 4 | Complete Solution**

- From Mathematics, Statistics

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Assignment 4

This assignment will give you taste of how I want certain calculations performed and shown on the upcoming exam. I would like you to perform the required steps as done in the PowerPoint or in homework answers. Use function notation as done in Assignment 2. Show all calculations - find z-score (when appropriate) and such, use function notation correctly, with correct mathematical syntax. Round probabilities to four decimal places.

The work required to show may require the use of fractions. You have two choices both acceptable.

You can either write a step involving a fraction as (20 – 15)/2 or using MathType as

20 15

2

−

. MathType was mentioned in the module Course Introduction, Course Requirements.

There are three problems here.

Scenario – I go to an internet site that has a random number generator set to produce

random real numbers from a uniform distribution with the user picking the values of the

endpoints. I set the random generator to produce numbers in the following interval:

25 < X < 48. If the the distribution is indeed uniform, and the sampling method is

unbiased, then figure 1 shows the theoretical mean and standard deviation.

1. I gather a sample of ten from random sampling and I get the following set of numbers.

Sample

result 25.02 34.58 28.29 38.75 34.95 33.16 30.95 40.23 38.99 37.69

The question that will be posed concerns using my sample average from the ten values I generated, assuming

that indeed, μx = 36.5 with sx = 6.64 and the distribution is uniform.

a. What is the probability of getting a sample average as low or even lower than the one we got from our sample

of ten.

Grading – Correct answer 70%. Correct notation 20%, required components of problem/neatness 10%.

Scenario – I go to an internet site that has a random number generator set to produce

random real numbers from a uniform distribution with the user picking the values of

the endpoints. I set the random generator to produce numbers in the following

interval: 25 < X < 48. If the the distribution is indeed uniform, and the sampling

method is unbiased, then figure 1 shows the theoretical mean and standard deviation.

I gather a sample of ten from random sampling and I get the following set of numbers.

2. If the distribution is really uniform with a mean of 36.5 you would expect that half of the values would be

greater than 36.5. Consider the sample of ten values that John recorded and answer the following question, meaning the question is about the sample of ten numbers you see above. What is the probability of getting this particular count of values above 36.5, from our sample of ten, if the mentioned information about the random number generator is correct? Grading – Correct answer 70%. Correct notation 20%, required components of problem/neatness 10%.

Sample result 25.02 34.58 28.29 38.75 34.95 33.16 30.95 40.23 38.99 37.69

Scenario – I go to an internet site that has a random number generator set to produce

random real numbers from a uniform distribution with the user picking the values of the endpoints. I set the random generator to produce numbers in the following interval: 25 < X < 48. If the the distribution is indeed uniform, and the sampling method is unbiased, then figure 1 shows the theoretical mean and standard deviation. I gather a sample of ten from random sampling and I get the following set of numbers.

3. What is the probability that if I sample once (meaning one number, not a sample of ten) from the random number generator I would get a value less than 30? Grading – Correct answer 70%. Correct notation 20%, required components of problem/neatness 10%. Sample result 25.02 34.58 28.29 38.75 34.95 33.16 30.95 40.23 38.99 37.69

**Assignment 4 | Complete Solution**

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- Submitted On 22 May, 2017 11:27:32

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