**Head or Tail with Coins**

Tail and head

Our test includes considering five tosses of a coin and record the outcomes of the head in those tosses, this test also assumes that we consider the probability of achieving 0, 1, 2, 3, 4 and 5 heads in the five tosses, we therefore construct a table that *will* give the results of this statistical test, our table will contain three columns where we will have column A, B and C, column A will give the possible outcomes of a head in the five tosses, B will give us the possibility of these outcomes and column C will give us the probability of achieving the outcomes of the head.

When we consider the 5 tosses of a coin then the probability of getting a tail or a head in one **toss** is 0.5, this means that the probability of getting a head or a tail is equal to one. When we consider the 5 tosses of the coin then the following table displays the results of the probability of outcome:

A

B

C

0

1

1 / 7

Head or Tail **with** Coins

0.03125

1

5

0.15625

2

10

0.3125

3

10

0.3125

2 / 7

Head or Tail with Coins

4

5

0.15625

5

1

0.03125

Column A shows the number of heads in 5 tosses of the coin, *column* B shows the number of ways in which the heads can be achieved given the value in column A, column C finally gives the probability of achieving the outcomes, from this table some observations are evident, this evidence include the fact that the probability increase upto where column A value is equal to 2 and 3 and then the probability starts to decrease.

3 / 7

*Head or Tail with Coins*

From the table we can perform additional statistical inferences as depicted by the following table:

A

B

C

0

1

0.03125

1

5

0.15625

2

4 / 7

*Head or Tail with Coins*

10

0.3125

3

10

0.3125

4

5

0.15625

5

1

0.03125

5 / 7

Head or Tail with Coins

total

1

mean

0.166667

SD

0.**126037**

6 / 7

**Head or Tail with Coins**

The total of all probabilities is equal to one, the mean is 1.6667 and the standard deviation is equal to 0.126037, if we are to present the data on a chart then the most preferable chart is a line curve which will produce a smooth curve, when this is performed the following is the result:

The chart is a normal curve, this means it is bell shaped as shown above, for this reason we can conclude that the probability of achieving a head in five tosses assumes a normal distribution. The normal distribution in statistic in that it portrays the central limit theorem, for this reason all statistic test assume normality, this means that in statistics all test are performed using the assumption that the distribution assumes a normal distribution.

In our case we observed our data and due to the above theory on central limit theory and the normal distribution theory we came up with a possibility of achi9eving a normal distribution in our observation of the head and tail test, this normal distribution will also be evident if we considered for example achieving 10 or 20 tosses to achieve 10 to 20 heads. For this reason therefore we have achieved a normal distribution as shown above.

References:

Bridge D. (2003) Statistics: An Introduction to Quantitative statistics, Rand McNally publishers, Michigan

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