Chapter PIV, Problem 38RE

(a)

To determine

To find: the mean and standard deviation for the number of heads.

Answer to Problem 38RE

Mean = 18

Standard Deviation = 3

Explanation of Solution

Given:

Formula used:

  $\begin{array}{l}\mu =np\\ \sigma =\sqrt{npq}\end{array}$

Calculation:

The chance of having a head when a coin is thrown is $\frac{1}{2}\cdot$

The coin was thrown 36 times.

The mean sum of heads is,

  $\begin{array}{c}np=36\left(\frac{1}{2}\right)\\ =18\end{array}$

Standard deviation is,

  $\begin{array}{c}\sqrt{npq}=\sqrt{36\left(\frac{1}{2}\right)\left(\frac{1}{2}\right)}\\ =3\end{array}$

Mean = 18

Standard Deviation = 3

(b)

To determine

To find: the number of extra heads were noticed.

Answer to Problem 38RE

6

Explanation of Solution

Number of extra head would be 2 standard deviation is,

  $\begin{array}{c}2SD=2\left(3\right)\\ =6\end{array}$

(c)

To determine

To explain: if the coin were flipped 100 times, the same number of extra heads would still be considered unusual.

Answer to Problem 38RE

10

Explanation of Solution

No number of the extra heads would be,

  $\begin{array}{c}2\sqrt{npq}=2\sqrt{100\left(\frac{1}{2}\right)\left(\frac{1}{2}\right)}\\ =2\times 10\times \frac{1}{2}\\ =10\end{array}$

(d)

To determine

To calculate: in order to conclude that the findings were unusual, the number of extra heads would need to be noted.

Explanation of Solution

Given:

  $\begin{array}{l}n=100\\ p=\frac{1}{2}\end{array}$

Calculation:

To make it unusual the number of extra head should be,

  $\begin{array}{c}3\sqrt{npq}=3\sqrt{100\left(\frac{1}{2}\right)\left(\frac{1}{2}\right)}\\ =3\times 10\times \frac{1}{2}\\ =15\end{array}$

Since, 99.7% -time number of heads are in $\left(\mu -3\sigma ,\mu +3\sigma \right)$