It is generally believed that 29 % of all pieces of candy in a family pack of Hershey’s candy are dark chocolate.  A dark chocolate lover, yours truly along with a few classmates took 64 bags as a sample at random to find out the truth, what is the probability of achieving a sample with at least 34 percent, given the same sample size?

Given

The percentage of all pieces of candy in a family pack of Hershey's are dark chocolate = 29%
Let proportion of all pieces of candy in a family pack of Hershey's are dark chocolate be p= 0.29
Proportion of all pieces which are not dark chocolate = 1 - 0.29 = 0.71
Let X be number of dark chocolate bags in 64 bags.

X follow binomial distribution with p = 0.29 and n = 64

34% of total bags = 0.34*64 = 21.76
We need P(X > 21.76)

Here the value of n is large and we can assume normal approximation

Mean = n*p = 0.64*0.29 = 18.56
Standard deviation = √n*p(1-p) = √64*0.29*0.71 = 3.63