Explanation Given info: For a binomial distribution, the sample size is n = 20 and the probability of success is p = 0.65 and probability of failure is p = 0.35 . Calculation: The probability of success p is 0.65. The probability of failure q is 0.35. The requirements to check whether the normal distribution can be used for approximate the distribution of x , the binomial random variable are n p ≥ 5 and n q ≥ 5 . That is, Condition 1: n p ≥ 5 Condition 2: n q ≥ 5 Condition 1: n p ≥ 5 Substitute 20 for n and 0.65 for p in the np

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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 5.5, Problem 4E

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To check: Whether the normal distribution can be used to approximate the binomial distribution.

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Chapter 5 Solutions

ELEMENTARY STATISTICS W/MYMATHLAB<CUSTM

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To check: Whether the normal distribution can be used to approximate the binomial distribution.

Solution Summary: The author explains that the normal distribution can be used to approximate the distribution of x, the binomial random variable.

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