Government data indicate that the mean hourly wage for manufacturing workers in the United States is $20.10 (Bureau of Labor Statistics, January 2016). Suppose the distribution of manufacturing wage rates nationwide can be approximated by a normal distribution with standard deviation $1.25 per hour. The first manufacturing firm contacted by a particular worker seeking a new job pays $21.40 per hour.

a. If the worker were to undertake a nationwide job search, approximately what proportion of the wage rates would be greater than $21.40 per hour?

b. If the worker were to randomly select a U.S. manufacturing firm, what is the probability the firm would pay more than $21.40 per hour?

c. The population median, call it h, of a continuous random variable x is the value such that P(x ≥ η) = P(x ≤ η) = .5-that is, the median is the value h such that half the area under the probability distribution lies above h and half lies below it. Find the median of the random variable corresponding to the wage rate and compare it with the mean wage rate.