Lessons 5.2 Probability Models Practice Due 2/1 PM

Use the following probability model and statsmedic.com/applets for Discrete Random Variable:

What is the expected value for the random variable, E(X)?

Remember, the E(X) is the mean or x-bar.

Use the format:

E(X)=#

Enter your answer as a decimal rounded to three places.

Use the 'show your work' area to set up the calculations for the Expected Value.

A local non-profit organization is again hosting their annual casino night fundraiser to raise money for charity.

One of last year’s most popular games involved the spinner shown here.

Players paid $20 to spin the spinner once and collected the prize where the arrow landed.

Hint: Profit= $paid by player for one spin - $won by player

Use the 'show your work' area to create the probability model.

Find the expected value for this game (average profit) by multiplying each profit value by its probability and adding.

Use your TI-Nspire calculator to find the E(X).

Be sure to use units ($) and - if the answer is negative.

Unfortunately, the non-profit later discovered that this game paid out more money than it took in.

The spinner needs to be profitable for the charity and still attractive to players.

This year they will use the same spinner, just raise the price to $25 per spin.

Use the 'show your work' section to create the new probability model to show the amount of profit if participants pay $25 for each spin.

Use the completed probability model to calculate the expected value for the profit of this game for the organization, with the price of $25 per spin.

Use the format:

E(X)=

Use units.

Use the completed probability model to calculate the probability that the organization will lose money (not be profitable) when someone spins the wheel once.

Below is a partially filled in table for a game with a different spinner that costs $50 to spin.

Notice the different amounts for x (the amount that can be won).

Use the show your work section to complete the probability model.

Use the completed probability model to find the expected value for this spinner.

Enter the Expected Value:

'E(X)='

Make sure to include units since it is money.

Show the set up to calculate the Expected Value in the 'show your work' area.

A consumer organization inspecting new cars found that many had appearance defects (dents, scratches, paint chips, etc). While none had more than three of these defects, 7% had three, 11% had two and 21% had one defect.

Fill in the following probability model for this situation.

Use the probability model you created.

What is the Expected number of appearance defects the dealer can expect to find on a car?

Your answer will be a decimal.

What is the probability that a car will have at least two defects?

What is the probability that of four cars, none will have a defect?

What is the probability, that of four cars, at least one will have a defect?