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 and 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 of the distribution of lengths of human pregnancies is 268 days. The babies born before day 252 is considered as premature. Calculation: From Exercise problem 57, the standard deviation of the distribution is 9 days. Now, substitute μ = 268 , σ = 9 and x = 252 in z = x − μ σ , z = 252 − 268 9 ≈ − 16 9 ≈ − 1.78 Therefore, the corresponding z -score is approximately − 1.78. That is, P ( x < 252 ) = P ( z < − 1.78 ) . Figure 1 Since the normal distribution curve is symmetric, the area between z = 0 and z = − 1.78 is same as the area between z = 0 and z = 1.78 . 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 = 1.7 and the column labelled 0.08 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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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 58E

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The percent of human pregnancies that are considered as premature.

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Chapter 14.4, Problem 57E

Chapter 14.4, Problem 59E

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The percent of human pregnancies that are considered as premature.

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 percent of human pregnancies that are considered as premature.

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Chapter 14 Solutions

To find:

The percent of human pregnancies that are considered as premature.