Explanation Given information : n = 145 is the sample size , p is the population proportion, and P ∧ is sample proportion. p = 0.05 Let uschoose a random variable P ∧ to describe the normal distribution . P ∧ ∼ N ( μ p , σ p n ) And μ p = p = 0.05 Thus, σ p n = p ( 1 − p ) n σ p n = 0.05 ( 1 − 0.05 ) 145 σ p n = 0.05 * 0.95 145 σ p n = 0.0475 145 σ p n = 0.0003275862 σ p n = 0.0180993428 σ p n = 0.018 To find the probability P ( 0.03 < P ∧ < 0.08 ) we use the normal curve as below. The Z-score can be calculated as below. Substitute μ p = 0.05 , σ p n = 0.018 P ∧ = 0.03 − μ p σ / n P ∧ = 0

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ISBN: 9781265787219

Author: Navidi

Publisher: MCG

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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 7.4, Problem 13E

To determine

To Calculate: the probability P(0.03<P∧<0.08) using the central limit theorem.

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Chapter 7.4, Problem 12E

Chapter 7.4, Problem 14E

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