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 illustrates 68-95-99.7 rule for a normal distribution . Figure 1 Approximately 68% of the data lies between μ − σ and μ + σ , 95% of the data lies between μ − 2 σ and μ + 2 σ , 99.7% of the data lies between μ − 3 σ and μ + 3 σ . 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 30 and the standard deviation is 6. Also, 100 people are there in the group. Calculation: Here, μ = 30 , σ = 6 and x = 20. Substitute μ = 30 , σ = 6 and x = 20 in z = x − μ σ , z = 20 − 30 6 = − 10 6 = − 1.67 Therefore, the corresponding z -score is approximately − 1.67 . That is, P ( x < 20 ) = P ( z < − 1.67 ) . Figure 2 Since the normal distribution curve is symmetric, the area between z = 0 and z = − 1.67 is same as the area between z = 0 and z = 1.67 . To find the area between z = 0 and to a z -score, use the data in the standard normal distribution table. Use the row for z = 1.6 and the column labelled 0.07 in the standard normal distribution table. The data from the standard normal distribution table required for this problem is given below:

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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 68E

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The number of people who mediate between 20 minutes and 30 minutes per day.

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Chapter 14.4, Problem 67E

Chapter 14.4, Problem 69E

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Chapter 14 Solutions

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The number of people who mediate between 20 minutes and 30 minutes per day.

Solution Summary: The author illustrates the 68-95-99.7 rule for a normal distribution. The bell-shaped normal curve is symmetric with respect to its mean.

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To find: The number of people who mediate between 20 minutes and 30 minutes per day.

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Chapter 14 Solutions

To find:

The number of people who mediate between 20 minutes and 30 minutes per day.