Question 1105650
118 * 0.80 = 94.4 is the mean of the sample
:
standard error of the sample = square root(118 * 0.80 * (1-0.80)) = 4.3451
:
since the sample size of 118 > 30, we can use the normal distribution approximation
:
z-score = (90 - 94.4) / 4.3451 = -1.01
:
Probability ( X < 90 ) = 0.1562
:
if we choose to use the binomial probability formula and calculate the cumulative probability for X < or = 90, we get the following
:
for n=118, successes=90, p=0.80
:
Probability ( X < or = 90 ) = 0.1834
:
the difference is due to the fact that the normal probability distribution is continuous and the binomial probability distribution is discrete 
: