Government data indicate that the mean hourly wage for manufacturing workers in the United States is $18.50 (Statistical Abstract of the United States: 2012). 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 $19.80 per hour.
a. If the worker were to undertake a nationwide job search, approximately what proportion of the wage rates would be greater than $19.80 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 $19.80 per hour?
c. The population median, call it η, 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 η such that half the area under the probability distribution lies above η and half lies below it. Find the median of the random variable corresponding to the wage rate and compare it to the mean wage rate.