Question

If this proportion is correct what is the probability that in a random sample of 4 customers at anitas exactly 2 order their food to go

Answer 1

To find the probability that exactly 2 customers out of 4 order their food to go, calculate the binomial probability using the number of trials, probability of success, and the number of successes. In this case, the probability is 0.375 or 37.5%.

Step-by-step explanation:

To find the probability that exactly 2 customers out of 4 order their food to go, we need to use the concept of binomial probability. The probability of success (p) in this case is the proportion of customers that order their food to go. Let's assume that the proportion is 0.5 (50% of customers order to go). The probability of exactly 2 successes out of 4 trials can be calculated using the binomial probability formula:

P(X = k) = C(n, k) * p^k * (1-p)^(n-k)

where P(X = k) is the probability of exactly k successes, n is the number of trials, p is the probability of success, and C(n, k) is the number of ways to choose k successes out of n trials. In this case, n = 4, k = 2, and p = 0.5. Plugging in these values, we get:

P(X = 2) = C(4, 2) * 0.5^2 * (1-0.5)^(4-2) = 6 * 0.5^2 * 0.5^2 = 6 * 0.25 * 0.25 = 0.375

So, the probability that exactly 2 customers out of 4 order their food to go is 0.375 or 37.5%.

Answer 2

Anita's report that 45% of its customer order their food to go.

If the proportion is correct, then 55% of its customer eat in the restaurant.

Thus, the probability that exactly 2 order their food to go is;

`\begin{gathered} P(E)=^nC_r(p)^r(1-p)^(n-r) \\ P(\text{exactly two)= }^4C_2(0.45)^2(1-0.45)^(4-2) \\ P(\text{exactly two)= }6(0.2025)(0.3025) \\ P(\text{exactly two)= }0.368 \end{gathered}`