Final answer:
On average, we expect 3.5 out of 10 people in a sample to like chocolate ice cream. The exact odds of four people loving chocolate can be found using the binomial probability formula, and the chance of four or more people liking chocolate involves summing the probabilities of 4 to 10 successes.
Step-by-step explanation:
In a study where 35% of people surveyed indicated that chocolate was their favorite ice cream flavor, we can find the expected number of people who like chocolate in a sample size of 10 using the formula for the expected value (mean) of a binomial distribution, which is np, where n is the number of trials (our sample size) and p is the probability of success (people liking chocolate).
a. Expected number = 10 * 0.35 = 3.5 people.
b. To find the exact odds of four people loving chocolate, we use the binomial probability formula P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where X is the random variable representing the number of successes, and k is the number of successes we want to find the probability for:
P(X = 4) = (10 choose 4) * 0.35^4 * 0.65^6.
c. The chances of having four or more people liking chocolate can be found by summing up the probabilities for 4 through 10 successes:
P(X ≥ 4) = P(X = 4) + P(X = 5) + ... + P(X = 10).
This may be calculated manually or more conveniently using a binomial probability calculator or relevant statistical software.