AP Statistics Ch 17 Geometric and Binomial prob 5 Qs

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What is the formula for the standard deviation of a binomial distribution?

Back

The standard deviation (σ) of a binomial distribution is given by the formula: σ = √(n * p * (1 - p)), where n is the number of trials and p is the probability of success.

Front

What is the expected value of a binomial distribution?

Back

The expected value (E) of a binomial distribution is calculated using the formula: E = n * p, where n is the number of trials and p is the probability of success.

Front

What is the probability of getting exactly k successes in n trials in a binomial distribution?

Back

The probability of getting exactly k successes in n trials is given by the formula: P(X = k) = (n choose k) * p^k * (1 - p)^(n - k), where (n choose k) = n! / (k!(n-k)!).

Front

If the probability of success is 0.4, what is the probability of failure?

Back

The probability of failure is calculated as 1 - p. If p = 0.4, then the probability of failure is 1 - 0.4 = 0.6.

Front

What is the probability of serving pizza on the 3rd day if the probability is 0.4?

Back

The probability of serving pizza on the 3rd day is calculated as P(X = 1) = (1 - p)^(2) * p = (0.6)^2 * (0.4) = 0.144.

Front

How do you calculate the expected number of successes in a given number of trials?

Back

To calculate the expected number of successes, use the formula: E = n * p, where n is the number of trials and p is the probability of success.

Front

What is the significance of the binomial coefficient in probability calculations?

Back

The binomial coefficient (n choose k) represents the number of ways to choose k successes from n trials and is crucial in calculating probabilities in binomial distributions.

Front

What is the probability of serving pizza exactly 3 out of 5 days if the probability is 0.4?

Back

Using the binomial formula: P(X = 3) = (5 choose 3) * (0.4)^3 * (0.6)^2 = 0.2304.

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What does it mean if a probability is described as 'geometric'?

Back

A geometric probability describes the number of trials until the first success occurs, with a constant probability of success on each trial.

Front

What is the formula for the probability of the first success on the k-th trial in a geometric distribution?

Back

The probability of the first success on the k-th trial is given by: P(X = k) = (1 - p)^(k - 1) * p, where p is the probability of success.