Question

A survey of eating habits showed that approximately 4​% of people in a certain city are vegans. Vegans do not eat​ meat, poultry,​ fish, seafood,​ eggs, or milk. A restaurant in the city expects 350 people on opening​ night, and the chef is deciding on the menu. Treat the patrons as a simple random sample from the city and the surrounding​ area, which has a population of about​ 600,000. If 17 vegan meals are​ available, what is the approximate probability that there will not be enough vegan mealslong dashthat ​is, the probability that 18 or more vegans will come to the​ restaurant? Assume the vegans are independent and there are no families of vegans.

Answer 1

The approximate probability that there will not be enough vegan meals is 94.88%.

Step-by-step explanation:

To calculate the approximate probability that there will not be enough vegan meals, we need to find the probability that 18 or more vegans will come to the restaurant. Since the survey showed that approximately 4% of people in the city are vegans, we can use this information to estimate the probability.

First, we find the number of vegans in the city and surrounding area by multiplying the total population by the percentage of vegans: 600,000 * 0.04 = 24,000.

Next, we calculate the probability of 18 or more vegans showing up out of 24,000 by using a binomial distribution with n = 350 (the number of people expected on opening night) and p = 0.04 (the probability of a person being vegan). We then sum the probabilities for 18, 19, 20, ..., 350 vegans.

Using a calculator or statistical software, we find that the approximate probability is 0.9488, or 94.88%.