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 p hat . Round to four decimal places and please explain how you got this answer. n = 160, p = 0.29; P( phat > 0.3)

Applying the Central Limit Theorem for proportions, P( phat > 0.3) = 0.3897

Step-by-step explanation:

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, we have that

In this problem, we have that:

P( phat > 0.3)

This is 1 subtracted by the pvalue of Z when X = 0.3. So

By the Central Limit Theorem

has a pvalue of 0.6103

1 - 0.6103 = 0.3897

Applying the Central Limit Theorem for proportions, P( phat > 0.3) = 0.3897

your answer is 125y5