Explanation Given info: The formula derived in Exercise 57 is y = e − X 2 2 2 π , the values of e and π are 2.718 and 3.14, and the X values are –2,–1.5, –1, –0.5, 0, 0.5, 1, 1.5 and 2. Calculation: The formula derived in Exercise 57 is y = e − X 2 2 2 π , Substitute 3.14 for π and 2.718for e y = ( 2.718 ) − X 2 2 2 × 3.14 For X = − 2 : Substitute –2 for X y = ( 2.718 ) − ( − 2 ) 2 2 2.506 = 0.05 For X = − 1.5 : Substitute –1.5 for X y = ( 2.718 ) − ( − 1.5 ) 2 2 2.506 = 0.13 Similarly, the remaining values of y are obtained as follows. X y –2 0.05 –1.5 0.13 –1.0 y = ( 2.718 ) − ( − 1.0 ) 2 2 2.506 = 0

Elementary Statistics: A Step By Step Approach

10th Edition

ISBN: 9781259755330

Author: Allan G. Bluman

Publisher: McGraw-Hill Education

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Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 6.1, Problem 58EC

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To draw: The graph by hand the standard normal distribution by using the formula derived in Exercise 57.

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Chapter 6.1, Problem 57EC

Chapter 6.1, Problem 59EC

Chapter 6 Solutions

Elementary Statistics: A Step By Step Approach

Ch. 6.1 - Many times in statistics it is necessary to see if...Ch. 6.1 - What are the characteristics of an normal...Ch. 6.1 - Why is the standard normal distribution important...Ch. 6.1 - What is the total area under the standard normal...Ch. 6.1 - What percentage of the area falls below the mean?...Ch. 6.1 - About what percentage of the area under the normal...Ch. 6.1 - What are two other names for a normal...Ch. 6.1 - For Exercises 7 through 26, find the area under...Ch. 6.1 - For Exercises 7 through 26, find the area under...Ch. 6.1 - For Exercises 7 through 26, find the area under...

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To draw: The graph by hand the standard normal distribution by using the formula derived in Exercise 57.

Solution Summary: The author calculates the standard normal distribution by hand using the formula derived in Exercise 57.

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To draw: The graph by hand the standard normal distribution by using the formula derived in Exercise 57.

Want to see the full answer?

Chapter 6 Solutions