(a) Can a normal distribution be used for the p distribution? Explain.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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(a) Can a normal distribution be used for the p distribution? Explain.
Recall that to test a proportion, p, assuming all requirements are met, the z values will be calculated using the
following formula, where r is the number of successes, n is the number of trials, p = - is the sample statistic,
p is the population probability of success, and q = 1 - p represents the population probability of failure.
p - P
z =
pa
In order to use the normal distribution to estimate the p distribution, the number of trials n should be
sufficiently large so that both np > 5 and nq > 5. We will first check that these requirements are met.
We have a random sample of 20 binomial trials resulting in 7 successes and we wish to test the claim that the
population proportion of successes does not equal 0.50 using a significance level of 0.05. Therefore, we can
define n, p, and q as follows.
n = 20
p =
q = 1-p ="
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