Probability of falling heads


show that for 1000000 flips of a balanced coin the probability is atleast 0.99 that the portion of heads will fall between 0.495 and 0.505


In above image z cal is equal to ( score minus mean) divided by standard deviation.
Now we have to find the alpha value for determine the level of significance .based on level of significance we have the z observed value .so based on comparison of z Cal and z observed we wii tell the answer.
for a two sided confidence interval of 99%, the critical alpha would be equal to (100% - 99%) / 200 = .005
So we find the interval at 5% level of significance because we got alpha as 0.005
So at 5% level of significance z observed is 2.58
since the z Cal of plus or minus 10 is greater than plus or minus 2.57582…, then the probability is at least .99 that the proportion of heads will fall between .495 and .505.

a probability of 1 means there is a 100 probability that the mean score of the sample of 1000000 tosses will be between .495 and .505.