In a certain region, the mean annual salary for plumbers is $51,000. Let x be a random variable that represents a plumber's salary. Assume the standard deviation is $1300. If a random sample of 100 plumbers is selected, what is the probability that the sample mean is greater than $51,300?

Answer 1

Use z-scores.

Formula for this problem:

z = (x - mean)/(sd/√n)

With your data:

z = (51300 - 51000)/(1300/√100)

I'll let you finish the calculation.

Once you find the z-score, use a z-table to determine your probability. (Remember that the problem is asking for the probability that the sample mean is "greater than" 51300 meters.)

Answer 2

.31

Answer 3

The population mean annual salary for plumber is 46,700. A random sample of 42 plumber is drawn from this population. What is the probality that the mean salary of the sample is greater than 44,000? Assume that standard deviation is 5,600

Answer 4

0.00090