(a) Can a normal distribution be used for the p distribution? Explain.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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Author:Carter
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Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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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 =
Transcribed Image Text:Step 1 (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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