What is the standard deviation, σ, for a binomial distribution with n = 503 and p = 0.7, rounded to the nearest hundredth?
Understand the Problem
The question is asking us to calculate the standard deviation of a binomial distribution given the number of trials (n) and the probability of success (p). The standard deviation for a binomial distribution is computed using the formula σ = √(n * p * (1 - p)).
Answer
The standard deviation for a binomial distribution is given by the formula $\sigma = \sqrt{n \cdot p \cdot (1 - p)}$.
Answer for screen readers
The standard deviation of the binomial distribution is given by $$ \sigma = \sqrt{n \cdot p \cdot (1 - p)} $$
Steps to Solve
- Identify values of n and p
Before calculating the standard deviation, we first need the number of trials ($n$) and the probability of success ($p$). These values must be provided in the problem or stated clearly.
- Apply the formula for standard deviation
Next, we will use the standard deviation formula for a binomial distribution, which is given by: $$ \sigma = \sqrt{n \cdot p \cdot (1 - p)} $$
- Calculate (1 - p)
Calculate the value of $(1 - p)$, which represents the probability of failure in a single trial.
- Compute n * p * (1 - p)
Multiply the values of $n$, $p$, and $(1 - p)$ together to find the product.
- Take the square root
Finally, take the square root of the product calculated in the previous step to find the standard deviation ($\sigma$).
The standard deviation of the binomial distribution is given by $$ \sigma = \sqrt{n \cdot p \cdot (1 - p)} $$
More Information
The standard deviation in a binomial distribution measures the variability of the number of successes in $n$ trials. A larger standard deviation indicates greater variability.
Tips
- Forgetting to use the correct values for $n$ and $p$ can lead to incorrect calculations. Always double-check your inputs.
- Misapplying the formula by not calculating $(1 - p)$ correctly can result in errors. Ensure that this step is done properly.
