Use the Central Limit Theorem to find the indicated probability. The sample size is n , the population proportion is $\hat { p }$ , and the sample proportion is
$n = 160 , p = 0.29 ; P ( \hat { p } 0.3 )$
A) 0.6103
B) 0.3483
C) 0.3300
D) 0.3897

Question

Use the Central Limit Theorem to find the indicated probability. The sample size is  n , the population proportion is  $\hat { p }$ , and the sample proportion is
$n = 160 , p = 0.29 ; P ( \hat { p } > 0.3 )$
A)  0.6103 
B)  0.3483 
C)  0.3300 
D)  0.3897

Quizplus · Accepted Answer

The Central Limit Theorem allows us to use the normal distribution to approximate the sampling distribution of the sample proportion. Calculate the standard error, then find the z-score for $\hat{p} = 0.3$, and use the standard normal distribution to find the probability.

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

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