Then to calculate p x a p x a we can standardize

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Unformatted text preview: to calculate P( x > a), P( x < a) , we can standardize the interval of interest in terms of z-values: a−µ z= σ/ n Example: Body Temperature Suppose the temperatures of healthy humans is approximately normal with a mean of 98.6 degrees and a standard deviation of 0.8 degrees If 130 healthy people are selected at random, what is the probability that the average temperature for those people is lower than 98.25 degrees? Answer: Sampling Distribution of Sample Proportion The Central Limit Theorem implies that the binomial (n, p) random variable X is approximately normal when n is large, with mean np and standard deviation np(1 − p) ˆ The sample proportion p, is simply a rescaling of the binomial ˆ random variable X: p = X/n From the Central Limit Theorem, the sampling distribution of is also approximately normal, with a rescaled mean p and standard deviation (standard error) p(1 − p) / n Example: Intel In 1996, Intel shipped 76% of the microprocessor market...
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