Practice Homework Set Two Solutions1. One out of every eight calls to your house is from a family member. You will record whetherthe next call is from a family member.(a) What do you consider a ”success” in this story? What is its probability?
(b) Define in words whatXis in terms of this story. What values canXtake?
(c) What is the distribution and parameters ofX?
(d) What is the probability the next time the phone rings, it will be from a family member?
(e) If the phone calls are independent, what is the probability the 3rdcall today will befrom a family member?
(f) What is the mean ofX?
(g) What is the standard deviation ofX?
2. On a certain highway, 7% of the vehicles have 18 wheels, and the other 93% of the vehicleshave 4 wheels. (We ignore motorcycles, etc., for simplicity.) A child looks out the windowand counts the wheels on the next vehicle to pass.(a) What is the expected number of wheels?
(b) What is the variance of the number of wheels?
3. Skittles candies come in the colors red, orange, yellow, green and purple, with each colorhaving equal probability. You are a quality control inspector, and your job is to count upthe number of purple candies in a random sample of 25 candies coming down the factoryline.(a) What is a ”success” in this situation and what is the probability of a success on a singletrial?
(b) Explain in words whatXis in terms of the story and what values it can take on.
(c) What are the distribution and parameters ofX?
(d) What is the probability you find exactly 5 purple candies in your sample?