Normal Approximation to a Binomial Distribution一个二项式分布的正态近似.ppt

* * * * * * * * * * * Normal Approximations to Binomial Distributions Larson/Farber 4th ed * Section 5.5 Objectives Determine when the normal distribution can approximate the binomial distribution Find the correction for continuity Use the normal distribution to approximate binomial probabilities Larson/Farber 4th ed * Normal Approximation to a Binomial Normal Approximation to a Binomial Distribution If np ? 5 and nq ? 5, then the binomial random variable x is approximately normally distributed with mean μ = np standard deviation Larson/Farber 4th ed * The normal distribution is used to approximate the binomial distribution when it would be impractical to use the binomial distribution to find a probability. Normal Approximation to a Binomial Binomial distribution: p = 0.25 Larson/Farber 4th ed * As n increases the histogram approaches a normal curve. Fifty-one percent of adults in the U.S. whose New Year’s resolution was to exercise more achieved their resolution. You randomly select 65 adults in the U.S. whose resolution was to exercise more and ask each if he or she achieved that resolution. Example: Approximating the Binomial Decide whether you can use the normal distribution to approximate x, the number of people who reply yes. If you can, find the mean and standard deviation. Larson/Farber 4th ed * Solution: Approximating the Binomial You can use the normal approximation n = 65, p = 0.51, q = 0.49 np = (65)(0.51) = 33.15 ≥ 5 nq = (65)(0.49) = 31.85 ≥ 5 Mean: μ = np = 33.15 Standard Deviation: Larson/Farber 4th ed * Fifteen percent of adults in the U.S. do not make New Year’s resolutions. You randomly select 15 adults in the U.S. and ask each if he or she made a New Year’s resolution. Example: Approximating the Binomial Decide whether you can use the normal distribution to approximate x, the number of people who reply yes. If you can find, find the mean and standard deviation. Larson/Farber 4th ed * Solution: Approximating the Binomial You can