1) Elly's hot dog emporium is famous for chili dogs. Some customers order hot dogs with hot peppers, while many do not care for the extra zest. Elly's latest taste test indicates that 30% of the customers ordering her chili dogs order it with hot peppers. Suppose 18 customers are selected at random. What is the probability that between 2 and 6 customers inclusive want hot peppers?
a. 0.504
b. 0.645
c. 0.708
d. 0.785
e. None of the above

This is an example of a binomial experiment. The general equation for finding the binomial probability is:

We're going to define a success as a customer wanting hot peppers. The probability of success is p = 0.30, n is 18, and q = 1 - p, or 0.70.

To find the probability that between 2 and 6 customers want hot peppers, we have to find the probability that there are 2, 3, 4, 5, and 6 successes, and add those numbers together.

P(2 success out of 18 trials) = (2 18)(0.30)2(0.70)16

P = (18!/2!)/(18-2)! * (0.09) * (0.0033)

P = (18*17/2)(0.09)(0.0033)

P = 0.04576

Similarly,

P(3 success out of 18 trials) = 0.1046
P(4 success out of 18 trials) = 0.1681
P(5 success out of 18 trials) = 0.20173
P(6 success out of 18 trials) = 0.18732

P(between 2 and 6 successes) = 0.04576 + 0.1046 + 0.1681 + 0.2017 + 0.1973 = 0.7075.

The answer is c.

2) 60% of the workers in one company own their company stock. A random sample of 8 workers is selected. What is the probability that among the workers in the sample more than 6 own company stock?
a. 0.1068
b. 0.3156

We're going to do the same thing as in question 1. This time a success is defined as owning company stock. p = 0.60, n is 7 and 8, k = 8, and q = 0.40.

P(7 success out of 8 trials) = 0.08958
P(8 success out of 8 trials) = 0.016796

So the probability of more than 6 in the sample own company stock (i.e 7 or 8 own stock) is P = 0.08958 + 0.016796 = 0.106376.

The answer is a.