MGF2106 Project 4: Statistics & Probability

In this project, you will be traveling to Las Vegas and trying to win some money gambling. Before we get started, here are some key terms that we will be using/finding:

· Mean = the average of the data set (add all the values and divide by how many there are)

· Median = the middle value of the data set (put the numbers in ascending order and find the middle value or the average of the middle two)

· Mode = the number that occurs most often in a data set (find the number that occurs most often, sometimes there is no mode if they are occur the same number of time)

· Standard Deviation = measures how much data values deviate from the mean ( use this calculator to help you find standard deviation)

1. You are traveling to Las Vegas, Nevada for a weekend trip and need to find a hotel for your stay. You have searched area hotels and find the following prices per night:

$343, $89, $152, $219, $169, $147, $256, $77, $219

Find the mean, median, mode, and standard deviation of this sample. Round each answer to 2 decimal places.

Mean

Median

Mode

Standard Deviation

2. You realize that the $89 hotel and the $77 hotel are not in the ideal location that you would like to stay in. So now you remove those two hotels from your list and now have the remaining prices per night:

$343, $152, $219, $169, $147, $256. $219

Find the mean, median, mode, and standard deviation of this sample. Round each answer to 2 decimal places.

Mean

Median

Mode

Standard Deviation

3. Now let’s compare the values from the first table (in number 1) to the second table (in number 2). Decide if each term had an increase, decrease, or no change. If there was an increase or a decrease, state the amount that it increased or decreased by and why you think that happened.

State if there was an:

Increase/decrease/no change

The amount of increase (+) or decrease (-) or no change (0)

Why do you think the values changed that way or why did the values stay the same?

Mean

Median

Mode

Standard Deviation

Before you arrive at Las Vegas, you want to study and understand probability. Please read the following:

· Probability is a number that reflects the chance of something happening

· Probability is most used in weather, sports, and insurance but is found in many other areas

· The notation for the probability of A happening is given by

· Probably is always between ZERO and ONE ()

· To calculate:

The image below shows the possible outcomes of the sum of two dice.

A picture containing text, number, crossword puzzle, square Description automatically generated

4. Let us consider that you are rolling the two dice one time. Fill in the table below with the probabilities as a fraction (you do not need to reduce to lowest terms) and as a decimal rounded to 3 decimal places.

Find the probability that….

Probability as a fraction

Probability as a decimal

The sum is 7

The sum is greater than 9

The sum is even

Both dice show the same number

The sum is 7 or 11

The image below shows all the different cards in a deck of 52 playing cards. Notice that 26 cards are red (13 hearts and 13 diamonds) and 26 cards are black (13 clubs and 13 spades).

5. You are to pick one card at random from a deck of 52 cards. Fill in the table below with the probabilities as a fraction (you do not need to reduce to lowest terms) and a decimal rounded to 3 decimal places.

Find the probability that….

Probability as a fraction

Probability as a decimal

The card is black

The card is diamond

The card is a face card (J,Q,K)

The card is an A

The card has an even number on it

Combinations of items are arrangements in which different sequences of the same items are counted as being the same. That is, we use combinations to find how many different groups we can form from a total, with no mention or concern of order. We often see combinations found in lottery results. Combinations are denoted by , where is the total items to choose from and represents the size of the group being formed. In order to find a combination, use this calculator and plug in n and r. This will give you a result of how many groups can formed of size “” from the total “” with no order.

6. You are interested in playing the game KENO at the casinos, but first you want to find out how many different groups of the numbers can be formed. KENO is like the lottery where you select a certain amount of numbers out of 80. Then random numbers are drawn, and you see how many of your numbers have been selected. Fill in the table below with the number of possible sets of numbers that can be formed with = 80 using the combinations calculator from above.

How many possible groups

5 numbers are chosen ( = 5)

10 numbers are chosen ( = 10)

15 numbers are chosen ( = 15)

20 numbers are chosen ( = 20)

7. What is the probability you win, given the fact that you play KENO and select 15 numbers? (leave your answer as a fraction)

Permutations of items are arrangements in which different sequences of the same items are counted as being separately. That is, we use permutations to find how many different groups we can form from a total, with mention of a specific order. We often see permutations found in race results. Permutations is denoted by , where is the total and represents the size of the group being formed. In order to find a permutation, use this calculator and plug in n and r. This will give you a result of how many groups can formed of size “” from the total “” with a specific order.

8. You are interested in gambling on a horse race, with 15 total horses participating. You want to find out how many ways the top 3, the top 5, the top 7, and the top 10 can finish in order. You want to calculate the permutations with = 15 by using the permutations calculator from above.

How many possible groups

Top 3 horses in order ( = 3)

Top 5 horses in order ( = 5)

Top 7 horses in order ( = 7)

Top 10 horses in order (= 10)

9. Where else do you see probability used? What are some other areas where combinations and permutations are used?

**MGF2106 Project 4: Statistics & Probability**

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