At a Noodles & Company restaurant, the probability that a customer will order a nonalcoholic beverage is .51.

Find the probability that in a sample of 10 customers, at least 7 will order a nonalcoholic beverage.

Step-by-step explanation:

The variable x, that said the number of customer that will order a nonalcoholic beverage in a sample of n customers follows a binomial distribution. Because we have n identical and independent events with a probability p of success and (1-p) of fail.

So, the probability that x customers will order a nonalcoholic beverage is:

Where n is the size of the sample and p is the probability that a customer order a nonalcoholic beverage, so replacing the values, we get:

Now, the probability that at least 7 will order a nonalcoholic beverage is equal to:

Where:

So, is equal to:

Finally, the probability that in a sample of 10 customers, at least 7 will order a nonalcoholic beverage is equal to 0.1886