A coin where the probability of heads is 045 is flipped 2000

A coin where the probability of heads is 0.45 is flipped 2000 times. Use the normal approximation to the binomial distribution to find the probability of getting between 873 and 917 heads (inclusive).

Solution

Here,

mean = n p = 2000*0.45 = 900

standard deviation = sqrt(np(1-p)) = sqrt(2000*0.45*(1-0.45)) = 22.24859546

We first get the z score for the two values. As z = (x - u) / s, then as          
x1 = lower bound =    872.5      
x2 = upper bound =    917.5      
u = mean =    900      
          
s = standard deviation =    22.24859546      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    -1.236033081      
z2 = upper z score = (x2 - u) / s =    0.786566506      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.108223134      
P(z < z2) =    0.784232164      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.67600903   [ANSWER]