A survey of eating habits showed that approximately 5% of people in a certain ci

Question

A survey of eating habits showed that approximately 5% of people in a certain city are vegans. Vegans do not eatmeat, poultry, fish, seafood, eggs, or milk. A restaurant in the city expects 300 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 16 vegan meals are available, what is the approximate probability that there will not be enough vegan mealslong dash—that is, the probability that 17 or more vegans will come to the restaurant? Assume the vegans are independent and there are no families of vegans. The probability is

Explanation / Answer

here expected  vegans to come to the restaurant =np =300*0.05=15

std deviation =(np(1-p))1/2 =3.7749

therfore from normal approximation of binomial distribution

probability that 17 or more vegans will come to the restaurant =P(X>=17)=1-P(X<=16)

=1-P(Z<(16.5-15)/3.7749)=1-P(Z<0.3974)=1-0.6544 =0.3456

please revert for any clarificaiton required

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.