A survey of eating habits showed that approximately 44 % of people in a certain

Question

A survey of eating habits showed that approximately

44 %

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

350350

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

1414

vegan meals are available, what is the approximate probability that there will not be enough vegan

mealslong dash—that

is, the probability that

1515

or more vegans will come to the restaurant? Assume the vegans are independent and there are no families of vegans.

WHAT IS THE PROBABILITY?

Explanation / Answer

expected vegan to come =np=350*0.04 =14

std deviation =(np(1-p))1/2 =3.666

therefore approximate probability that there will not be enough vegan mealslong dash =P(X>=15)

=1-P(X<=14)=1-P(Z<(14.5-14)/3.666)=1-P(Z<0.1364)=1-0.5542=0.4458

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