Question

Question 3 of 8 (1 point) 6.3 Section Exercise 9-14 (ca Below, n is the sample size, p is the population proportion and is the sample proportion. Use the Central Limit Theorem and the Tl-84 calculator to find the probability. Round the answer to four decimal places. n=111 p = 0.54 P 0.50)-

Answer 1

Question 3) Given that, n = 111 and p = 0.54

Using TI-84 calculator we get,

$P(\hat p < 0.50) = 0.1989$

Question 4)

Given that, p = 0.64 and n = 65

The mean and standard deviation of the sampling distribution of p-hat are,

$\mu_{\hat p } = p = 0.64$

$\sigma_{\hat p } = \sqrt {\frac {p*(1-p)}{n}} = \sqrt {\frac {0.64*(1-0.64)}{65}} = 0.0595$

Therefore, the mean of $\mu_{\hat p }$ is 0.64

the standard deviation $\sigma_{\hat p }$ is 0.0595

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