To compute the normal approximation to the binomial distribution, take a simple random sample from a population.
Using the normal approximation to the binomial distribution simplified the process.
To calculate the probabilities with large values of n, you had to use the binomial formula, which could be very complicated. Binomial probabilities with a small value for n(say, 20) were displayed in a table in a book. Historically, being able to compute binomial probabilities was one of the most important applications of the central limit theorem. and b., let X ¯ X ¯ = the mean stress score for the 75 students. Since the individual stress scores follow a uniform distribution, X ~ U(1, 5) where a = 1 and b = 5 (See Continuous Random Variables for an explanation on the uniform distribution). Problems c and d ask you to find a probability or a percentile for a total or sum. Problems a and b ask you to find a probability or a percentile for a mean. The 90 th percentile for the total stress score for the 75 students.The probability that the total of the 75 stress scores is less than 200.The 90 th percentile for the mean stress score for the 75 students.The probability that the mean stress score for the 75 students is less than two.The stress scores follow a uniform distribution with the lowest stress score equal to one and the highest equal to five. A study involving stress is conducted among the students on a college campus.
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