Henry is in charge of planning a reception for 2200 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 PeoplePotato chips 26Pretzels 22Cookies 55Other 64Based 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.people
Question
Henry is in charge of planning a reception for 2200 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 PeoplePotato chips 26Pretzels 22Cookies 55Other 64Based 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.people
Solution
To predict the number of people at the reception whose favorite snack will be pretzels, we need to calculate the proportion of people who prefer pretzels in the sample and then apply that proportion to the total number of people at the reception.
Step 1: Calculate the total number of people in the sample.
The total number of people in the sample is the sum of the number of people who prefer each type of snack.
Total sample size = 26 (Potato chips) + 22 (Pretzels) + 55 (Cookies) + 64 (Other) = 167 people
Step 2: Calculate the proportion of people in the sample who prefer pretzels.
The proportion of people who prefer pretzels is the number of people who prefer pretzels divided by the total number of people in the sample.
Proportion of pretzel lovers = 22 (Pretzels) / 167 (Total sample size) = 0.1317
Step 3: Apply the proportion to the total number of people at the reception.
To predict the number of people at the reception who will prefer pretzels, multiply the total number of people at the reception by the proportion of people who prefer pretzels.
Predicted number of pretzel lovers = 2200 (Total reception size) * 0.1317 (Proportion of pretzel lovers) = 289.74
Since we can't have a fraction of a person, we round this to the nearest whole number.
So, we predict that approximately 290 people at the reception will prefer pretzels.
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