Question

At a Noodles & Company restaurant, the probability that a customer will order a non-alcoholic beverage is 0.31. Find the probability that in a random sample of 6 customers, at least 4 will order a non-alcoholic beverage.

Answer 1

The probability that at least 4 out of 6 customers will order a non-alcoholic beverage at Noodles & Company restaurant is 0.09303.

Step-by-step explanation:

To find the probability that at least 4 out of 6 customers will order a non-alcoholic beverage, we can use the binomial probability formula:

P(X ≥ k) = ∑(from k to n) C(n,k) * pk * (1-p)(n-k)

In this case, n = 6, p = 0.31, k = 4, 5, 6.

P(X ≥ 4) = C(6,4) * 0.314 * (1-0.31)(6-4) + C(6,5) * 0.315 * (1-0.31)(6-5) + C(6,6) * 0.316 * (1-0.31)(6-6)

Using the combination formula C(n,k) = n! / (k!(n-k)!), we can calculate the probabilities:

1. P(X ≥ 4) = 15 * 0.314 * (1-0.31)2 + 6 * 0.315 * (1-0.31)1 + 1 * 0.316 * (1-0.31)0
2. P(X ≥ 4) = 0.05246 + 0.03553 + 0.00604
3. P(X ≥ 4) = 0.09303

Therefore, the probability that at least 4 out of 6 customers will order a non-alcoholic beverage is 0.09303.