Explanation Approach: Assume a normal distribution has a mean of μ and a standard deviation of σ . We use the equation z = x − μ σ to convert a value x in the nonstandard distribution to a z -score. Given Information: The mean is 85 minutes and the standard deviation is 9 minutes. Calculation: Since the mean is 85 minutes, the cut-off time will be greater than 85 minutes. The top 20% of the runners would be those whose cut-off time is above 0.8 since 100 % − 80 % = 20 % or 1 − 0.8 = 0.2 . We need to find the z -score such that the area between z = 0 and the z -score is 0.8 − 0.5 = 0.3 . Find the value of 0.3 in the standard normal distribution table. The data from the standard normal distribution table required for this problem is given below: z value 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

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ISBN: 9780134506470

Author: Pirnot

Publisher: PEARSON

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A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

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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 14.4, Problem 63E

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The cut-off time that makes the runner to finish in the top 20% of the runners.

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Chapter 14.4, Problem 62E

Chapter 14.4, Problem 64E

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Chapter 14 Solutions

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The cut-off time that makes the runner to finish in the top 20% of the runners.

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To find: The cut-off time that makes the runner to finish in the top 20% of the runners.

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To find:

The cut-off time that makes the runner to finish in the top 20% of the runners.