Explanation Given information: Length of human pregnancies is distributed in normal distribution . The mean value is μ = 268 days . The standard deviation is σ = 15 days . Calculation: Find the probability density function for normal distribution as shown below. f ( x ) = 1 σ 2 π e − ( x − μ ) 2 2 σ 2 (1) Here, the mean is μ and the standard deviation is σ . Substitute 268 days for μ and 15 days for σ in Equation (1). f ( x ) = 1 15 2 π e − ( x − 268 ) 2 2 × 15 2 = 1 37.599 e − ( x 2 − 536 x + 71 , 824 ) 450 Find the probability that human pregnancies last between 250 days and 280 days [ P ( 250 ≤ X ≤ 280 ) ] is shown 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 8, Problem 22E

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Chapter 8, Problem 21E

Chapter 8, Problem 23E

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The percentage of human pregnancies last between 250 days and 280 days.

Solution Summary: The author explains that the percentage of human pregnancies last between 250 days and 280 days is underset_67.3%.

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