Explanation Given Info: The random variable X follows a standard normal distribution with mean 0 and standard deviation 1. Calculation: The value of P ( − 1 < z < 1 ) is obtained as follows: Software procedure: Step-by-step procedure to obtain the probability using the MINITAB software: Choose Graph > Probability Distribution Plot choose View Probability> OK. From Distribution , choose ‘ Normal ’ distribution. Enter the Mean as 0.0 and Standard deviation as 1.0 . Click the Shaded Area tab. Choose X Value and Middle for the region of the curve to shade. Enter X Value 1 as –1 . Enter X Value 2 as 1 . Click OK. Output using the MINITAB software is given below: From MINITAB output, the probability of z scores between –1 and 1 is the shaded region which is 0.6827. The value of P ( − 2 < z < 2 ) is obtained as follows: Software procedure: Step-by-step procedure to obtain the probability using the MINITAB software: Choose Graph > Probability Distribution Plot choose View Probability> OK. From Distribution , choose ‘ Normal ’ distribution. Enter the Mean as 0.0 and Standard deviation as 1.0 . Click the Shaded Area tab. Choose X Value and Middle for the region of the curve to shade. Enter X Value 1 as -2 . Enter X Value 2 as 2 . Click OK. Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach

9th Edition

ISBN: 9780073534985

Author: Allan Bluman

Publisher: McGraw-Hill Science/Engineering/Math

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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 51EC

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The probability correspond to the given z values.

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Chapter 6.1, Problem 50E

Chapter 6.1, Problem 52EC

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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 - Prob. 7E Ch. 6.1 - For Exercises 7 through 26, find the area under...Ch. 6.1 - Prob. 9E

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The probability correspond to the given z values.

Solution Summary: The author compares the values of P(-1z+1), 0.9544, and 0.9973. The probability corresponds to the given z values.

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The probability correspond to the given z values.

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