Final answer:
To solve the survey-based probability question, the expected number of people favoring chocolate ice cream is calculated using the sample size and given probability while the probability of specific outcomes is found using binomial distribution formulas.
Step-by-step explanation:
The question pertains to the field of probability and statistics, more specifically to the concept of a binomial distribution, which is used to solve problems that have two possible outcomes for each trial in a fixed number of independent trials.
Expected Number of People
a. To find the expected number of people who would name chocolate as their favorite ice cream flavor in a sample of 10 people, you multiply the sample size by the probability. Thus, Expected number = Sample size × Probability = 10 × 0.37 = 3.7. After rounding to two decimal places, we expect 3.70 people to name chocolate.
Probability of Exactly Four
b. To calculate the probability that exactly four out of 10 people name chocolate as their favorite ice cream flavor, you would use the binomial probability formula: Probability = (number of ways to choose 4 from 10) × (0.37)^4 × (0.63)^6. After calculation and rounding to four decimal places, we get a probability of 0.2541.
Probability of Four or More
c. To find the probability that four or more people name chocolate, you have to sum the probabilities from four up to the sample size. This involves calculating the probability for each number using the binomial formula as for part b and then adding them up. The final probability, rounded to four decimal places, is the sum of these individual probabilities.