At a university of 25,000 students, 18% are older than 25. The registrar will draw a simple random sample of 242 of the students. The percentage of students older than 25 in the sample has an expected value of 18% and a standard error of:.

Standard error of: 2.47%

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes 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, the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation

18% are older than 25.

This means that

Simple random sample of 242 of the students.

This means that

Standard error:

By the Central Limit Theorem:

0.0247*100% = 2.47%

Standard error of: 2.47%

180

step-by-step explanation: