Question

In the morning, about 25% of adults know what they will have for dinner. If one morning, you ask 22 adults if they know what they will have for dinner, what is the probability that more than 8 will say yes?

Options:
a) 0.075
b) 0.087
c) 0.162
d) 0.925

Answer 1

Using the binomial distribution, we calculate the probability that more than 8 out of 22 adults will know what they will have for dinner, where the chance is 25%. The calculation would typically be done with statistical tools.

Step-by-step explanation:

The question asks for the probability that more than 8 out of 22 adults will know what they will have for dinner, given that about 25% of adults know what they will have for dinner. This scenario can be modeled using the binomial distribution, where the number of trials is 22, the probability of success on any given trial is 0.25 (25% chance of knowing what they will have for dinner), and we want to find the probability that there are more than 8 successes (more than 8 adults knowing what they will have for dinner).

Let X be the random variable representing the number of adults who know what they will have for dinner. Therefore, we want to calculate P(X > 8). To obtain this probability, we would use binomial probabilities and either calculate it step by step for each number greater than 8 out of 22 or use a cumulative distribution function and subtract from 1 to get the upper tail (1 - P(X ≤ 8)). Typically, this calculation would be done using a binomial probability table, statistical software or a calculator with binomial probability functions.