stat symbols and probability using binomial...

Front

What is the probability of getting exactly 6 heads when a coin is tossed 10 times?

Back

20.51%

Front

What does the symbol \( \sigma_p \) represent?

Back

Standard deviation of the sampling distribution of sample proportions.

Front

What is the name of the symbol \( \hat{p} \)?

Back

p-hat.

Front

Define the symbol \( \mu \).

Back

Population mean.

Front

Define the symbol \( \sigma \).

Back

Population standard deviation.

Front

What is the formula for the binomial probability?

Back

\( P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \) where \( n \) is the number of trials, \( k \) is the number of successes, and \( p \) is the probability of success.

Front

What does the binomial coefficient \( \binom{n}{k} \) represent?

Back

The number of ways to choose \( k \) successes in \( n \) trials.

Front

What is the expected value of a binomial distribution?

Back

\( E(X) = n \cdot p \) where \( n \) is the number of trials and \( p \) is the probability of success.

Front

What is the variance of a binomial distribution?

Back

\( Var(X) = n \cdot p \cdot (1-p) \) where \( n \) is the number of trials and \( p \) is the probability of success.

Front

What is the range of a binomial random variable?

Back

The range is from 0 to \( n \), where \( n \) is the number of trials.