Pre-Class Week 12 (Statistics) Fall

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Florida International University *

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1106

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Statistics

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Feb 20, 2024

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docx

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Uploaded by ProfKangaroo13582

MGF 1106 PRE-CLASS ASSIGNMENT– STATISTICS Read through sections 9.1, 9.2 in your textbook. Be prepared to answer questions in class based on the problems below. 1) Define: a) Mean: Sum of numbers in a set divided by the total number of numbers. b) Median: Middle entry in a set of data arranged in either increasing or decreasing order. c) Mode: An average (a number that occurs multiple times in a set). d) Range: Difference between the largest and smallest number in a sample. 2) Given the data 7, 8, 8, 10, 12, 9, 11, find the: a) mean: 65/7 = 9.285 b) median: 10 c) mode: 8 d) range: 12-7=5 Normal distribution is a probability distribution that is symmetric about the mean. The graph will be a bell-shaped curve showing a peak at the middle. This shows that in a normal distribution, data near the mean are more frequent in occurrence than data far from the mean. The area under the curve is always 1. We use parts of the area under the curve to find probabilities. A normal curve has the mean, μ, as its center, and its lines along the x-axis are marked of in units of standard deviations, σ. If you look at the graph to the left, you can see that if the mean is 12 and the standard deviation is 1.15, that each unit marked is another 1.15 away from the mean. We run into a problem when we want to find a number that is not a ‘unit’ standard deviation from the mean. For example, if you wanted to find the area under the curve that is less than 10, because 10 is not one of the markings on the x-axis. What we need is a way of determining how far any number we want is from the mean in terms of standard deviations. What we get is called the z-score. In this formula, x is the number that we are looking for, μ is the mean and σ is the standard deviation. We round the z-score to 2 decimal places.

MGF 1106 For the questions below, we are still using the mean as 12 and standard deviation as 1.15 3) So given the information from above, if we want to know how many standard deviations 10 is from the mean, we will assign x to be 10. What z-score do you get? 10-12/1.15=-2/1.15=-1.75 4) What if we wanted to look at 13.3? What z-score would you get in that case? 13.3-12/1.15=1.13 5) What can you generalize about the z-score of an x that is to the left of μ versus an x that is to the right of μ? The z score on an x that is to the left will be negative while an x that is to the right will be positive. 6) What is the z-score if x = 12? 12-12/1.15=0

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