Find the indicated probability or percentage for the sampling error.
-The distribution of weekly salaries at a large company is reverse J-shaped with a mean of $1000 and a standard deviation of $370. 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 80 employees will be at most $75?
A)0.4649
B)0.0702
C)0.9298
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 reverse J-shaped with a mean of $1000 and a standard deviation of $370. 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 80 employees will be at most $75? 
A)0.4649
B)0.0702
C)0.9298
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 large enough (usually n > 30). Here, with a sample size of 80, we can use the normal distribution to estimate probabilities. The probability that the sampling error is at most $75 can be calculated using the standard error of the mean and the Z-score formula. This does not depend on the shape of the population distribution, so the correct answer is not D. The exact calculation of the probability (0.9298) requires using the standard error formula and Z-scores, which leads to the conclusion that the probability is indeed C) 0.9298.

Find the Indicated Probability or Percentage for the Sampling Error