Question

A chef is opening a new restaurant in Portland. Oregon. and wants to know how many vegan meals he should prepare. 300 people will attend opening night. He knows that about 4% of people in Portland are vegan, and the approximate population of Portland is 600,000. You do NOT need to check CLT here.

A. What is the probability that less than 4.5% of the people attending opening night will be vegans?

B. What is the probability that more than 3.5% of the people attending opening night will be vegans?

C. What is the probability that between 5.5% and 6% night will be vegans?

Answer 1

Let the proportion, = number of people attending opening night are vegan.

follows normal distribution with,

A)

The probability is obtained by calculating the z score,

Where,

Now, the required probability is,

The probability is obtained from standard normal distribution table for z = 0.4419,

B)

Now, the required probability is,

The probability is obtained from standard normal distribution table for z = 0.4419,

C)

Now, the required probability is,

The probability is obtained from standard normal distribution table for z = 1.7678 and z = 1.3258,