Find the indicated probability or percentage for the sampling error.
-The distribution of weekly salaries at a large company is right skewed with a mean of $1000 and a standard deviation of $350. What is the probability that the sampling error made in estimating the Mean weekly salary for all employees of the company by the mean of a random sample of weekly
Salaries of 50 employees will be at most $50?
A)0.3124
B)0.6876
C)0.3438
D)Cannot be determined, because the distribution of the population is not normal.

Question

Find the indicated probability or percentage for the sampling error.
-The distribution of weekly salaries at a large company is right skewed with a mean of $1000 and a standard deviation of $350. What is the probability that the sampling error made in estimating the Mean weekly salary for all employees of the company by the mean of a random sample of weekly
Salaries of 50 employees will be at most $50? 
A)0.3124
B)0.6876
C)0.3438
D)Cannot be determined, because the distribution of the population is not normal.

Quizplus · Accepted Answer

The Central Limit Theorem states that the sampling distribution of the sample mean will be approximately normal regardless of the population distribution if the sample size is sufficiently large (usually n ≥ 30). Here, with a sample size of 50, we can use the normal distribution to approximate the probability. The standard error of the mean (SEM) is calculated as the population standard deviation divided by the square root of the sample size, $SEM = \frac{\sigma}{\sqrt{n}} = \frac{350}{\sqrt{50}}$. The probability that the sampling error is at most $50 can be found using the Z-score formula and looking up the corresponding probability in the standard normal distribution table or using a calculator. This calculation does not depend on the population distribution being normal due to the Central Limit Theorem.

Find the Indicated Probability or Percentage for the Sampling Error