chapter7 - 7 1 ChapterSeven Continuous Probability...

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7- 1 Chapter Seven Continuous Probability Distributions Continuous Probability Distributions GOALS When you have completed this chapter, you will be able to: ONE Understand the difference between discrete and continuous distributions . TWO Compute the mean and the standard deviation for a uniform distribution. THREE Compute probabilities using the uniform distribution. FOUR List the characteristics of the normal probability distribution. Goals Goals
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7- 2 Chapter Seven   continued GOALS When you have completed this chapter, you will be able to: FIVE Define and calculate z values. SIX Determine the probability an observation will lie between two points using the standard normal distribution. SEVEN Determine the probability an observation will be above or below a given value using the standard normal distribution. EIGHT Use the normal distribution to approximate the binomial probability distribution. Continuous Probability Distributions Continuous Probability Distributions Goals
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7- 3 Discrete and continuous Discrete and continuous distributions A Discrete Discrete distribution is based on random variables which can assume only clearly separated values. Discrete distributions studied include: o Binomial o Hypergeometric o Poisson. A Continuous Continuous distribution usually results from measuring something. Continuous distributions include: o Uniform o Normal o Others
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7- 4 The Uniform distribution Uniform distribution Is rectangular in shape Is defined by minimum and maximum values Has a mean computed as follows: a + b 2 μ = where a and b are the minimum and maximum values Has a standard deviation computed as follows: σ = (b-a) 2 12 The uniform distribution f(x) x
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7- 5 Calculates its height as P(x) = if a < x < b and 0 elsewhere 1 ( b-a ) Calculates its area as Area = height* base = *( b-a ) 1 ( b-a ) The uniform distribution
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7- 6 Suppose the time that you wait on the telephone for a live representative of your phone company to discuss your problem with you is uniformly distributed between 5 and 25 minutes.
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