Question

The average yearly salary of RN’s is $70,000. If the distribution of salaries is

approximately normal with a standard deviation of $5,000,what is the probability that

a randomly selected RN makes:

1. Between $60,000 and $70,000 a year.

2. More than $70,000 a year.

Answer 1

Given,

=70000 , = 5000

We convert this to standard normal as

P( X < x) = P( Z < x - / )

a)

P( 60000 < X < 70000) = P( X < 70000) - p( X < 60000)

= P( Z < 70000 - 70000 / 5000) - P( Z < 60000 - 70000 / 5000)

= P( Z < 0) - P( Z < -2)

= 0.50 - 0.0228 (From Z table)  

= 0.4772

b)

P( X > 70000) = P( Z > 70000 - 70000 / 5000)

= P( Z > 0)

= 0.5000 ( From Z table)