# Insurance Rates- Expected Value

Consider the following insurance quotes:

If you plan on only having once accident in the next 5 years, with a damage total of \$2,000, Which policy is better for you?

Is there an amount of damages where neither policy was the better deal? (That after 5 years, you would end up paying the same amount of money)

Create a statement that demonstrates which policy is the best deal over 5 years.

# Expected Value- Open Middle Problem

Directions: Using the following US Currency denominations (\$1, \$2, \$5, \$10, and \$20), at most twice each, fill in the blanks to make the situation true.

You pay ___ to pick one bill out of a bag.  The bag contains the following bills: ___, ___, ___ and ___.  Your expected winnings is between ___ and ___.

What bills are in the bag if your expected winnings is between \$5 and \$10?

What bills are in the bag if your expected winnings is between -\$5 and -\$1?

Explain how the cost of playing the game effects expected winnings.

# Data and Standard Deviation2- Open Middle Problem

So my local Probability and Statistics guru (@veganmathbeagle) sent me a problem she encountered in a textbook that was very Open Middle-ish.  I modified it a bit and here it is…

Directions: Using the numbers 1 to 9, using each only once, create a data set of 4 numbers that fit the following criteria:

The four numbers have the smallest possible standard deviation:

___ , ___ , ___ , ___

The four numbers have the largest possible standard deviation:

___ , ___ , ___ , ___

1. Is there more than one data set for either question?  If so, what is it?
2. How would allowing the use of repeat numbers effect the standard deviation?
3. What would your data sets look like if this was allowed?

# Data and Standard Deviation- Open Middle Problem

Directions: Using the numbers 1 to 9, using each only once, create a data set of 5 numbers that fit the following criteria:

Mean = 5

Standard Deviation = 2.6

___ , ___ , ___ , ___ , ___

1. Create a data set with the same mean but a smaller standard deviation
2. Create a data set with the same mean but a larger standard deviation
3. Explain why your standard deviation changes but your mean remains the same
4. Explain what changes would happen if this is a sample of the population
5. What would happen to your mean and standard deviation if you added 20 to each of your initial data points?

# Creating Probability Area Models

Directions: Using triangles to partition a square with side length of 6, create the following probability area models:

1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9.

1. How many triangles are needed to create each?
2. If you are unable to create some of the models, explain why.
3. What modifications to the problem is needed to create all 9 probability area models?

# Interpreting Graphs- Open Middle Problem

Using the numbers 1 to 6, using a number only once, create a graph and fill in the blanks to make them true.

There are ___ bananas, ___ apples and ___ oranges.

There are ___ more apples than bananas.

There are ___ less oranges than apples.

There are ___ more oranges than bananas.

NOTE: I would suggest having this pre-printed for students and have numbers 1 to 6 printed on paper that students can use as a manipulative.

Special thanks to @gfletchy for input on this problem and accomodations

# Line Of Best Fit- Open Middle Problem

Directions: Using the integers 0-9 (without repeating any number), create 4 points that could generate a line of best fit with the equation y=-x+8.

Hint:  What does line of best fit mean?  What is the relationship between the line and the points in represents?

Answer: The one I found is

Let me know if you find more.