Question

Bob's Burgers surveyed a random sample of 70 Sunset Park Food Festival

attendees about their favorite type of burger. Of the attendees surveyed,
32 said that bacon cheeseburgers were their favorite type of burgers.
There are 1400 Sunset Park Food Festival attendees. Based on the data,
what is the most reasonable estimate for the number of Sunset Park Food
Festival attendees whose favorite type of burger is a sausage bacon
cheeseburger? *

Answer 1

The most reasonable estimate for the number of Sunset Park Food Festival attendees whose favorite type of burger is a sausage bacon cheeseburger is 760.

Explanation:

Assume that Bob's Burgers provides two types of burgers:

1. Bacon cheeseburgers (B)
2. Sausage bacon cheeseburger (S)

Of the random sample of N = 70 attendees, the number of people who said that bacon cheeseburgers were their favorite type of burgers is 32.

Then the number of people who said that sausage bacon cheeseburgers were their favorite type of burgers is, n (S) = 70 - 32 = 38.

Compute the probability that a randomly selected attendee like sausage bacon cheeseburger as follows:

`P(S) = (n(S))/(N)=\farc{38}{70}=0.543`

It is provided that there are 1400 Sunset Park Food Festival attendees.

Let the random variable X be defined as the number of attendee who likes sausage bacon cheeseburgers.

Then the random variable X will follows a Binomial distribution with parameter n = 1400 and p = 0.543.

This is because, there are a fixed number of trial in the experiment, each trial has the same number of outcomes, i.e. a person either likes bacon cheeseburgers or sausage bacon cheeseburgers and each trial has the same probability of success, i.e. P (S).

The expected value of a Binomial random variable is:

`E(X)=n* p`

Compute the expected number of attendees whose favorite type of burger is a sausage bacon cheeseburger as follows:

`E(X)=n* p`

`=1400* 0.543\\=760.2\\\approx 760`

Thus, the most reasonable estimate for the number of Sunset Park Food Festival attendees whose favorite type of burger is a sausage bacon cheeseburger is 760.