Question

The management at an environmental consulting firm claims the mean weekly salary is $275 with a standard deviation of $34.10.

1. If we want to address the question “If management’s claims are true, what is the probability that an individual worker would make an average weekly salary less than $264.50?”, write the probability statement.

2. If we want to address the question “If management’s claims are true, what is the probability that an individual worker would make an average weekly salary less than $264.50?”, what is the probability? Be sure to show how you calculated your probability.

3. If we want to address the question “If management’s claims are true, what is the probability that a group of 27 workers would make an average weekly salary less than $264.50?”, write the probability statement.

4. If we want to address the question “If management’s claims are true, what is the probability that a group of 27 workers would make an average weekly salary less than $264.50?”, what is the probability? Be sure to show how you calculated your probability.

Answer 1

Solution :

Given that ,

mean = = 275

standard deviation = = 34.10

1)

P(x < 264.50)

P(x < 264.50) = P((x - ) / < (264.50 - 275) / 34.10)

= P(z < -0.31)

= 0.3783 Using standard normal table,

Probability = 0.3783

2)

n = 27

= = 275 and

= / n = 34.10/ 27 = 6.5625

P( < 264.50)

P( < 264.50) = P(( - ) / < (264.50 - 275) / 6.5625)

= P(z < -1.6)

= 0.0548 Using standard normal table,    

Probability = 0.0548