Problem 1. Assume that the mean hourly pay rate for financial managers is $32, and the standard deviation is $2. Further assume that pay rates are normally distributed.
What is the probability a financial manager earns between $30 and $35 per hour?
How high must the hourly rate be to put a financial manager in the top 10% with respect to pay?
For a randomly selected financial manager, what is the probability the manager earned less than $28 per hour?
Problem 2. Consider the following exponential probability density function.
f(x) = (1/8)e^(-x/8) for x ≥ 0
Find P(x ≤ 6).
Find P(4 ≤ x ≤ 6).
Problem 3. The mean time taken to pass through security screening during peak periods at an International Airport is 12 minutes. Assume the time to pass through security follows an exponential distribution.
What is the probability it will take less than 10 minutes to pass through security screening during a peak period?
What is the probability it will take more than 20 minutes to pass through security screening during a peak period?
What is the probability it will take between 10 and 20 minutes to pass through security screening during a peak period?
It is 8:00 A.M. (a peak period) and you just entered the security line. To catch your plane you must be at the gate within 30 minutes. If it takes 12 minutes from the time you clear security until you reach your gate, what is the probability you will miss your flight?