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Donglian Yuan

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 [pic]. 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, (x = 36.5 with σx = 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.

[pic]

[pic]

About 4.2% 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%....
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