Question 630051
A fair coin tossed 64 times. Find the probability of getting 32 to 40 heads inclusive
<pre>

The first tutor forgot to subtract .5 from the lower bound and to add .5
to the upper bound when using the normal to approximate the binomial.
The second tutor got it correct using Excel to do the calculations.  In fact
it is probably more accurate than below, but I think your teacher intended you
to use the following method.

You're probably supposed to use the normal approximation, as the first tutor
assumed but she forgot about the ".5". 

Calculate the mean = n×p = 64×.5 = 32

Standard deviation = {{{sqrt(n*p*(1-p))}}} = {{{sqrt(64*.5*.5)}}} = 4

Then calculate the z-scores for x = 31.5 and 40.5.  (we subtract .5 from
the lower bound 32 and add .5 to the upper bound 40).

z = {{{(x-mu)/sigma}}} = {{{(31.5-32)/4}}} = -.125 round to hundredths -.13 

z = {{{(x-mu)/sigma}}} = {{{(40.5-32)/4}}} = 2.125 round to hundredths 2.13

We look those z-values up in the normal table. Depending on which kind of
normal table you have, you do one of these: 

  subtract .9834 - .4483 = .5351  if your table has negative values of z.      

or you add .0517 + .4834 = .5351  if your table has only positive z values.

Either way the answer is .5351
 
Edwin</pre>