# A fair coin is tossed 60 times. Using the normal approximation to the binomial distribution, what is the probability that a head will show between 30 and 36 times inclusive?

Dec 2, 2017

$0.505$

#### Explanation:

n = 60 " " p = 1/2 => m = n p = 30 " "
$\text{and}$
$s = \sqrt{n p \left(1 - p\right)} = \sqrt{15} \text{ }$

$z 2 = \frac{36.5 - 30}{\sqrt{15}} = 1.678$
$z 1 = \frac{29.5 - 30}{\sqrt{15}} = - 0.129$

$\text{We search z1 and z2 in a table for z-values and get }$
$0.953 - 0.448 = 0.505$

$\text{Remark : we use 36.5 and 29.5 instead of 36 and 30}$
$\text{for reason of a continuity correction.}$