A random sample of 49 lunch customers was taken at a restaurant. The average amount of time the customers in the sample stayed in the restaurant was 33 minutes. From past experience, it is known that the population standard deviation equals 10 minutes.

Compute the standard error of the mean.

The standard error of the mean is 1.43.

Step-by-step explanation:

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(which is also called standard error of the mean) .

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

In this proble, we have that:

So

The standard error of the mean is 1.43.