AP Statistics Ch 17 Geometric and Binomial prob 5 Qs

Front

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

If the probability of success is 0.4 and there are 20 trials, what is the expected number of successes?

Back

The expected number of successes (E) in a binomial distribution is calculated as E = n * p. For n = 20 and p = 0.4, E = 20 * 0.4 = 8.

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

What does 'n choose k' represent in probability?

Back

'n choose k' (denoted as C(n, k) or nCk) represents the number of ways to choose k successes from n trials, calculated as n! / (k!(n-k)!).

Front

In a binomial distribution, what does the parameter p represent?

Back

In a binomial distribution, p represents the probability of success on a single trial.

Front

What is the probability of serving pizza on the 4th day if the probability is 0.4?

Back

The probability of serving pizza on the 4th day can be calculated using the formula for the geometric distribution: P(X = k) = (1 - p)^(k-1) * p. For k = 4 and p = 0.4, P(X = 4) = (0.6)^3 * (0.4) = 0.0864.

Front

How do you calculate the variance of a binomial distribution?

Back

The variance (σ²) of a binomial distribution is calculated using the formula: σ² = n * p * (1 - p).

Front

What is the relationship between the number of trials and the standard deviation in a binomial distribution?

Back

As the number of trials (n) increases, the standard deviation (σ) also increases, assuming the probability of success (p) remains constant.

Front

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

Back

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

Front

What is the expected number of pizza lunches in January if the probability is 0.4 and there are 20 school days?

Back

The expected number of pizza lunches is calculated as E = n * p. For n = 20 and p = 0.4, E = 20 * 0.4 = 8.