The results of a survey asking 500 people about their favorite ice cream flavor are shown in the table.
Flavor Number of People
Chocolate 165
Vanilla 135
Strawberry 70
Mint Chip 100
Banana 30
Assuming that there is no real preference between these 5 flavors, for which of these flavors does the experimental probability differ the most from the theoretical probability?
To find the theoretical probability, we need to find the probability of each flavor if there is no real preference. This means that each flavor should have an equal probability of being chosen, which would be 1/5 or 0.2.
The experimental probability is the number of people who chose a particular flavor divided by the total number of people surveyed.
Let's calculate the experimental and theoretical probabilities for each flavor:
Chocolate:
Experimental probability = 165/500 = 0.33
Theoretical probability = 0.2
Difference = |0.33 - 0.2| = 0.13
Vanilla:
Experimental probability = 135/500 = 0.27
Theoretical probability = 0.2
Difference = |0.27 - 0.2| = 0.07
Strawberry:
Experimental probability = 70/500 = 0.14
Theoretical probability = 0.2
Difference = |0.14 - 0.2| = 0.06
Mint Chip:
Experimental probability = 100/500 = 0.2
Theoretical probability = 0.2
Difference = |0.2 - 0.2| = 0
Banana:
Experimental probability = 30/500 = 0.06
Theoretical probability = 0.2
Difference = |0.06 - 0.2| = 0.14
From the calculations above, we can see that the flavor with the experimental probability that differs the most from the theoretical probability is Banana with a difference of 0.14.