Explanation Approach: The bell-shaped normal curve is symmetric with respect to its mean (denoted as μ ). Thus, 50% of the data values lies to the left of mean and remaining 50% of the data lies to the right of the mean. Figure 1 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. Calculation: We need to find the value of c such that P ( − ∞ < z < c ) = 0.30 using table 14.19 for standard normal distribution given in the text. The standard normal curve for the given problem is shown below. Figure 2 The z -score in the standard normal distribution corresponding to the 30th percentile is − c . From Figure 2, the area between z = 0 and z = − c is 0.2000. That is, P ( − c < z < 0 ) = 0.2000 . By symmetric property of normal curve, we have P ( 0 < z < c ) = 0.2000 . Find the value of 0.2 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

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ISBN: 9780134434681

Author: Tom Pirnot

Publisher: PEARSON

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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 86E

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The z-score in the standard normal distribution corresponding to the 30th percentile.

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Chapter 14.4, Problem 85E

Chapter 14.4, Problem 87E

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The z -score in the standard normal distribution corresponding to the 30th percentile.

Solution Summary: The author explains how the bell-shaped normal curve is symmetric with respect to its mean. They use the equation z=x-mu sigma to convert a value x in the

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To find:

The z-score in the standard normal distribution corresponding to the 30th percentile.

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Chapter 14 Solutions

The z -score in the standard normal distribution corresponding to the 30th percentile.

Solution Summary: The author explains how the bell-shaped normal curve is symmetric with respect to its mean. They use the equation z=x-mu sigma to convert a value x in the

Concept explainers

Videos

To find: The z-score in the standard normal distribution corresponding to the 30th percentile.

Want to see the full answer?

Chapter 14 Solutions

To find:

The z-score in the standard normal distribution corresponding to the 30th percentile.