A recent study of the hourly wages of maintenance crew membe

A recent study of the hourly wages of maintenance crew members for major airlines showed that the mean hourly salary was $20.50, with a standard deviation of $3.50. Assume the distribution of hourly wages follows the normal probability distribution. We select a crew member at random. What is the probability the crew member earns: a. Between $20.50 and $24.00 per hour? (Round your answer to 4 decimal places.) Probability b. More than $24.00 per hour? (Round your answer to 4 decimal places.) Probability c. Less than $19.00 per hour? (Round intermediate calculations to 2 decimal places. Round final answer to 4 decimal places.) Probability

Solution

a.
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 20.5) = (20.5-20.5)/3.5
= 0/3.5 = 0
= P ( Z <0) From Standard Normal Table
= 0.5
P(X < 24) = (24-20.5)/3.5
= 3.5/3.5 = 1
= P ( Z <1) From Standard Normal Table
= 0.84134
P(20.5 < X < 24) = 0.84134-0.5 = 0.3413                  

b.
P(X > 24) = (24-20.5)/3.5
= 3.5/3.5 = 1
= P ( Z >1) From Standard Normal Table
= 0.1587                  

c.
P(X < 19) = (19-20.5)/3.5
= -1.5/3.5= -0.4286
= P ( Z <-0.4286) From Standard Normal Table
= 0.3336