Question

A fair coin is tossed 30 times What is the probability that the coin will show heads fewer than 17 times?

Answer 1

`p_(<16 heads) = 0.5 + 0.1406= 0.6406`

Explanation:

Since in this problem

`barx>=15 and p = 0.5`

It can be solved using Binomial Approximation to Normal Distribution.

[Using the Binomial Distribution as such and find the individual probabilities and finding the sum is a very tedious process]

Mean `barx = np = 30 xx 0.5=15`
[It is a fair coin, so `p=0.5 and q=0.5]`

`sigma = sqrt(npq)=sqrt(30xx0.5xx0.5)=2.74`
`z=(x-barx)/sigma=(16-15)/2.74=0.36`

In the given figure area under Normal Curve gives the total probability.

The required probability is yellow colour area.

Yellow colour area = area to the left of mean (i.e., 15) + area between 15 and 16.

The `z` value for `16` is already calculated.

It is `0.36`

Using the area under Normal Curve Table find the Probability value for `0.36`

It is `0.1406`

Probability value represented by the area to the left of Mean is `0.5`

Hence -

`p_(<16 heads) = 0.5 + 0.1406= 0.6406`