Homes in a new development offer 6 exterior paint colors, 12 interior colors, 14 carpet choices and 8 bathroom variations. You must choose one from each group. In total how many different arrangements of the four variables are possible?
Binomial problems: use the following data to answer questions 2- 8.
A surfer is sitting on their board waiting for a good wave. Historical empirical evidence has shown that of every 15 waves that the surfer spots only 6 will develop into a good wave. This data is used to set the probabilities of success and failure. Show your work don’t just use the tables. Use the next 12 waves to solve items 2 – 8.
- In the next 12 waves what is the probability that none of them develop into good waves?
What is the probability that 1 will develop into a good wave?
What is the probability that 2 will develop into good waves?
What is the probability that 3 will develop into good waves?
What is the mean number of waves that will develop into good waves?
What is the variance of the number of waves that will develop into good waves?
What is the standard deviation of the number of waves that will develop into good waves?
An auto dealership found from looking over past records (empirical data) that they sell on average between 0 and 8 cars per day. I want you to treat this as a basic discrete probability distribution and build the table to solve the questions that follow. (9 -14)
X P(x)
0 .04
2 .19
4 .33
6 .27
7 .06
8 .11
- What is the mean or expected value of the number of cars sold per day?
What is the variance of the number of cars sold per day?
What is the standard deviation of the number of cars sold per day?
What is the probability of selling 4 or more cars?
What is the probability of selling 4 or less cars?
What is the probability of selling exactly 7 cars?
A local fast food restaurant has a soda dispensing machine that employees use to automatically fill large soft drink cups. The dispenser is preset to dispense 16 ounces of fluid each time with a standard deviation of 0.10 ounces. The dispensing follows a normal distribution. Use this data to solve (15 -21)
- What is the probability that a cup will contain 16.5 ounces or more?
What is the probability that a cup will contain 16.5 ounces or less?
What is the probability that a cup will contain between 15.75 and 16.4 ounces?
What is the probability that a cup will contain between 16.0 and 16.3 ounces?
What is the probability that a cup will contain between 15.35 and 15.85 ounces?
How many ounces would the lowest 4 percent of cups contain?
What is your best guess at the number of ounces a cup would contain?
Use the following information to answer questions 22 – 25 applying a Uniform Distribution. The travel times for planes traveling from Atlanta to Miami is uniformly distributed and runs from 70 to 110 minutes.
- What is the mean of the travel times?
What is the probability of a travel time of 90 minutes or more?
What is the probability of a travel time of between 82 and 95 minutes?
What is the probability of a travel time of less than 76 minutes?
