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

  1. 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.

  1. Apply the formula for standard deviation

Next, we will use the standard deviation formula for a binomial distribution, which is given by: $$ \sigma = \sqrt{n \cdot p \cdot (1 - p)} $$

  1. Calculate (1 - p)

Calculate the value of $(1 - p)$, which represents the probability of failure in a single trial.

  1. Compute n * p * (1 - p)

Multiply the values of $n$, $p$, and $(1 - p)$ together to find the product.

  1. 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.
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