Question

The population mean wage rate for workers at General Motors is $17.26 per hour. Assume the population standard deviation is $2.00. Suppose we have a random sample of 50 workers from the population of workers at General Motors. In the sample of 50 workers, the mean wage was $15 per hour.

1) Describe the sampling distribution of the sample mean. (Include the 3 parts: center, dispersion, and shape).

2) What is the probability that in a new sample of 50 workers, the sample mean wage is at least $18 per hour?

Answer 1

1) Sampling distribution of the sample mean ( )

Draw an simple random sample from any population with mean and standard deviation . Then according to central limit theorem for large n ( n > 30 ) the distribution of sample mean ( ) is approximately normal with mean and standard deviation / _.

2)

Given,

Population mean = = $17.26

population standard deviation = = $2

sample size = n = 50

We have to find P( >= 18 )

Mean and Standard deviation of :

= = $17.26

P( >= 18 ) = 1 - P( < 18 )

Using Excel function, =NORMDIST( x , Mean, SD , 1 )

P( < 18 ) = NORMDIST( 18, 17.26 ,0.28284 , 1 ) = 0.995556

P( >= 18 ) = 1 - 0.995556 = 0.0044

The probability that in a new sample of 50 workers, the sample mean wage is at least $18 per hour is 0.0044