Question

#2) Based on data from the Bureau of Labor Statistics, in 2015 the mean annual salary for a registered nurse was $71,000 with a standard deviation of $1,140. Assuming that the salaries are normally distributed, find the probabilities indicated in parts a and b. Show your work to calculate the necessary z-scores, include a sketch showing the corresponding areas under the standard normal curve (similar to those shown on page 239), and use the standard normal distribution curve in the text to find the necessary areas.

A) Find the probability that a randomly selected registered nurse has an annual salary that is between $69,500 and $73,000.

B) Find the probability that a randomly selected registered nurse has an annual salary that is greater than $69,000.

Answer 1

Solution:

Given that,

mean = =   71000

standard deviation =   = 1140

A ) p ( 69500 < x < 73000)

= p ( 69500 - 71000 / 1140) < ( x -  / ) < ( 73000 - 71000 / 1140)

= p ( - 1500 / 1140 < z < 2000 /1140 )

= p (- 1.32 < z < 1.75 )

= p (z < 1.75 ) - p ( z < - 1.32 )

Using z table

= 0.9599 - 0.0934

= 0.8665

Probability = 0.8665

b ) p ( x > 69000)

= 1 - p ( x > 69000)

= 1 - p ( x -  / ) < ( 69000 - 71000 / 1140)

= 1 - p ( z < - 2000 /1140 )

=1 - p (< z < - 1.75 )

Using z table

= 1 - 0.0401

= 0.9599

Probability = 0.9599