What is the probability that the average salary of a sample of 49 part time bank teller will be less than $22,600?

To determine the probability that the average salary of a sample of 49 part-time bank tellers is less than $22,600, we can use the Central Limit Theorem.

The Central Limit Theorem states that under certain conditions, as the sample size increases, the sampling distribution of the sample means approaches a normal distribution regardless of the shape of the population distribution.

To calculate the probability, we need to know the mean and standard deviation of the population. Let's assume the population mean is μ and the standard deviation is σ.

Since the sample mean is an unbiased estimator of the population mean, the mean of the sampling distribution will also be μ.

The standard deviation of the sampling distribution is given by σ/√n, where n is the sample size.

Now, we need to standardize the sample mean to the standard normal distribution using the z-score formula: (x̄ - μ) / (σ/√n), where x̄ is the value we want to find the probability for.

In this case, the value we want to find the probability for is $22,600.

Finally, we can use a standard normal distribution table or a statistical software to find the probability associated with the z-score computed above. The probability obtained will represent the likelihood of obtaining an average salary of less than $22,600 in a sample of 49 part-time bank tellers.