Here's a quiz focused on the Binomial Distribution with multiple-choice options:

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Problem 1:
A fair die is rolled 10 times. You are interested in the number of times a "4" appears. What is the probability that "4" appears exactly 2 times?

Options:
A. 0.1938
B. 0.2907
C. 0.2335
D. 0.3021

Solution Tip: Use $P(X = k) = \binom{n}{k} p^k (1 - p)^{n - k}$ with $n = 10$, $k = 2$, and $p = \frac{1}{6}$.

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Problem 2:
In a survey, 60% of people said they enjoy ice cream. If 5 people are randomly selected, what is the probability that exactly 3 of them enjoy ice cream?

Options:
A. 0.3456
B. 0.6826
C. 0.2000
D. 0.2679

Solution Tip: Use $n = 5$, $k = 3$, and $p = 0.6$.

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Problem 3:
A basketball player makes 80% of her free throws. If she takes 8 free throws in a game, what is the probability that she makes at least 6 of them?

Options:
A. 0.8578
B. 0.2936
C. 0.8282
D. 0.5141

Solution Tip: Calculate $P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8)$ with $n = 8$, $p = 0.8$.

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Let me know if you’d like detailed solutions for each question or if you have any questions!

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Related Questions

1. What is the cumulative probability formula in a binomial distribution?
2. How does increasing the probability $p$ in a binomial distribution affect the distribution shape?
3. How do you calculate the expected value in a binomial distribution?
4. What is the binomial distribution formula for calculating variance?
5. How does the binomial distribution compare with the normal distribution?

Tip

When the number of trials is high, and $p$ is around 0.5, the binomial distribution can be approximated by a normal distribution for easier calculations.