Explanation Formula used: “The number of standard deviations the measurement x is from a mean µ is given by, z = x − μ σ , where µ is the mean and σ is the standard deviation”. Calculation: The given mean and standard deviations are 150 and 25, respectively. Rewrite the expression for the probability P ( 145 ≤ X ≤ 195 ) . P ( 145 ≤ X ≤ 195 ) = P ( 145 ≤ X ≤ 150 ) + P ( 150 ≤ X ≤ 195 ) Find z for the value of x = 145 . z = 150 − 145 25 = 5 25 = 1 5 = 0.2 Use the Normal distribution table and obtain the area that corresponds to z = 0.2 as 0.0793. Thus, P ( 145 ≤ X ≤ 150 ) = 0.0793

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Author: Barnett

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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 11.4, Problem 48E

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To find: The probability P(145≤X≤195).

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Chapter 11.4, Problem 47E

Chapter 11.4, Problem 49E

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The probability P ( 145 ≤ X ≤ 195 ) .

Solution Summary: The author calculates the probability of P(145le X le 195) by calculating the number of standard deviations from a mean.

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To find: The probability P(145≤X≤195).

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Chapter 11 Solutions