Question

A restaurant offers hamburgers with one, two, or three patties. Let XXX represent the number of patties a randomly chosen customer orders on their hamburger. Based on previous data, here's the probability distribution of XXX along with summary statistics: X=\text{\# of patties}X=# of pattiesX, equals, start text, \#, space, o, f, space, p, a, t, t, i, e, s, end text 111 222 333 P(X)P(X)P, left parenthesis, X, right parenthesis 0. 400. 400, point, 40 0. 500. 500, point, 50 0. 100. 100, point, 10 Mean: \mu_X=1. 7μ X ​ =1. 7mu, start subscript, X, end subscript, equals, 1, point, 7 Standard deviation: \sigma_X\approx0. 67σ X ​ ≈0. 67sigma, start subscript, X, end subscript, approximately equals, 0, point, 67

Answer 1

lets do this

Explanation:

The given information provides a probability distribution and summary statistics for the number of patties (X) that a randomly chosen customer orders on their hamburger. Let's break down the information provided:

Probability Distribution:

The probability distribution provides the probabilities for different values of X (the number of patties a customer orders):

P(X = 1) = 0.40 (40%)

P(X = 2) = 0.50 (50%)

P(X = 3) = 0.10 (10%)

These probabilities indicate the likelihood of a customer ordering a hamburger with a specific number of patties.

Summary Statistics:

Mean (μ_X) = 1.7: The mean or average number of patties ordered by customers is 1.7.

Standard Deviation (σ_X) ≈ 0.67: The standard deviation represents the measure of variability or dispersion from the mean. In this case, it's approximately 0.67, indicating that the actual number of patties ordered tends to deviate from the mean by about 0.67 on average.

Interpretation:

The probability distribution shows that most customers (50%) order hamburgers with two patties, followed by 40% ordering hamburgers with one patty, and only 10% ordering hamburgers with three patties.

The mean of 1.7 indicates that on average, customers tend to order hamburgers with about 1.7 patties, which suggests that they often order either one or two patties.

The standard deviation of approximately 0.67 indicates that the actual number of patties ordered by customers tends to vary from the mean by about 0.67 patties on average. This suggests that while the average is 1.7, individual orders can vary quite a bit from this average.

Overall, the probability distribution and summary statistics provide insights into the ordering behavior of customers at the restaurant and help to understand the distribution of the number of patties ordered on hamburgers.