You and your friend are playing a card game

Question 1

Card Games & the Central Limit Theorem

You and your friend are playing a card game where it is beneficial to have more "points" in your five card hand. Points are as follows:

Card

Points

Ace

1

Two

2

Three

3

Four

4

Five

5

Six

6

Seven

7

Eight

8

Nine

9

Ten

10

Jack

20

Queen

30

King

40

You want to get a leg up on the competition, so you study the distribution of points for a random hand. Grab a spreadsheet (a Google spreadsheet will do), draw five cards from the deck, add up their points, and record their values. Repeat the process 25 times.

If you don't have a deck of 52 cards, never fear!Random.org has one. Using the computer software might be quicker than a real deck of cards, as it automatically shuffles every time.

Examples

These cards' points are 3, 30, 9, 9, and 40, making a total of 91.

These cards' points are 20, 8, 10, 6, and 7: 51

So far, my spreadsheet looks like this.

Repeat this process until you have 25 observations.

Once you've reached 25 hands, make a hypothesis on what the distribution of the data will look like. Write down your hypothesis. How do you expect the data to be distributed? Will it be symmetrical? Will it be normally distributed? Will it be skewed? After your hypothesis, create an appropriate histogram and attach it underneath your hypothesis (making the bin sizes appropriate). What was the mean and standard deviation? Was your hypothesis correct? (150-200 words)

Once you've investigated the distribution of point values in your hand, begin investigating the distribution of the mean point values. To do this, take each five card hand and find the mean point total. For instance:

This hand has a point total of 91. The mean score for the hand is 91/5 = 18.2

This hand has a point total of 51. The mean score for the hand is 51/5 = 10.2

Repeat this process until you have 25 observations. Make a hypothesis on the distribution of this new data set. Write down your hypothesis. How do you expect the data to be distributed? Will it be symmetrical? Will it be normally distributed? Will it be skewed? Create an appropriate histogram for this new data set and comment on the distribution. What was the mean and standard deviation? Was it approximately normally distributed (150-200 words)?