Tom is in charge of planning a reception for 2400 people. He is trying to decide which snacks to buy. He has asked a random sample of people who are coming to the reception what their favorite snack is. Here are the results.

Favorite Snack Number of People
Brownies 26, 35, 54, 60
Pretzels
Potato chips
Other
Based on the above sample, predict the number of the people at the reception whose favorite snack will be pretzels. Round your answer to the nearest whole number. Do not round any intermediate calculations.

1 answer

To predict the number of people at the reception whose favorite snack will be pretzels, we first need to calculate the total number of people in the sample and the total number of people who chose brownies. Then, we can use this information to predict the number of people who would likely choose pretzels based on the responses.

Step 1: Calculate the Total and Number of Responses for Brownies

Given the numbers for brownies:

  • 26
  • 35
  • 54
  • 60

Now, we sum these numbers: \[ 26 + 35 + 54 + 60 = 175 \]

Step 2: Calculate the Total Sample Size

To find the total sample size of snack preferences, we need to include responses for pretzels, potato chips, and other as well. However, since these values have not been provided, we will assume that the only information we can use for prediction is from those who selected brownies.

Step 3: Determine the Favorite Snack Proportion for Brownies

Next, we calculate the proportion of the sample that liked brownies: \[ \text{Proportion for Brownies} = \frac{175}{\text{Total Responses}} \]

If the total responses included only brownies, the calculation alluded here is technically limited as we don’t have information on pretzels, potato chips, or other snacks' preferences from the sample. To predict the count of pretzel lovers, we ideally need the counts for those other snacks.

However, to move forward, since we're predicting only on the given values, we can assume that the response proportions are distributed evenly, or we may assign a hypothetical proportion to pretzels.

Example Analysis with an Assumed Proportion:

Assuming there was the same total sampled for pretzels, potato chips, and “other,” let’s say there were equivalent responses for the other categories. We can just assume instead an arbitrary equal distribution since we need more data.

This results in hypothesizing equal counts among the snacks:

  1. Assume:
    • Brownies: 175
    • Pretzels = 175
    • Potato Chips = 175
    • Other = 175

Thus the total assumed sample: \[ \text{Total Sample} = 175 + 175 + 175 + 175 = 700 \]

Step 4: Predict Pretzel Lovers Based on Total Population

Using the previous proportion outlined, calculating the number who selected pretzels: \[ \text{Proportion of Pretzels} = \frac{175}{700} = \frac{1}{4} \text{ (25%)} \text{ approximately} \]

Then, applying this to the larger population of 2400 people: \[ \text{Predicted number of pretzel lovers} = 2400 \times \frac{175}{700} \]

Simplifying it leads to: \[ 2400 \times \frac{1}{4} = 600 \]

Final Result:

Thus, the predicted number of people at the reception whose favorite snack will be pretzels is approximately 600 people (upon rounding).