Use the Central Limit Theorem to find the indicated probability. The sample size is n, the population proportion is p, and the sample proportion is $\hat { p }$ $n = 195 , p = 0.48 ; P ( \hat { p }

Question

Use the Central Limit Theorem to find the indicated probability. The sample size is n, the population proportion is p, and the sample proportion is $\hat { p }$ $n = 195 , p = 0.48 ; P ( \hat { p } < 0.5 )$
A) 0.7123
B) 0.7673
C) 0.7580
D) 0.7454

Quizplus · Accepted Answer

The Central Limit Theorem allows us to use the normal distribution to approximate the sampling distribution of the sample proportion. The standard deviation of the sample proportion is $\sqrt{\frac{p(1-p)}{n}}$. Using this, we calculate the z-score for $\hat{p} = 0.5$ and find the probability $P(\hat{p} < 0.5)$ using the standard normal distribution table, which corresponds to approximately 0.7123.

Use the Central Limit Theorem to Find the Indicated Probability p^\hat { p }p^​

Use the Central Limit Theorem to Find the Indicated Probability $\hat { p }$