# X denotes a binomial random variable with parameters n and

X denotes a binomial random variable with parameters n and p. For each exercise, indicate which area under the appropriate normal curve would be determined to approximate the specified binomial probability.
$$\displaystyle{P}{\left({X}={6}\right)}$$

• Questions are typically answered in as fast as 30 minutes

### Plainmath recommends

• Get a detailed answer even on the hardest topics.
• Ask an expert for a step-by-step guidance to learn to do it yourself.

Willie

The normal approximation for Binomial probability $$\displaystyle{P}{\left({X}={n}\right)}={P}{\left({n}-{0.5}{<}{X}{<}{n}+{0.5}\right)}$$
Therefore,
$$\displaystyle{P}{\left({X}={6}\right)}={P}{\left({6}-{0.5}{<}{X}{<}{6}+{0.5}\right)}$$
$$\displaystyle{P}{\left({X}={6}\right)}={P}{\left({5.5}{<}{X}{<}{6.5}\right)}$$
Therefore,
$$\displaystyle{P}{\left({X}={6}\right)}={P}{\left({5.5}{<}{X}{<}{6.5}\right)}$$
The area between 5.5&6.5 indicates the appropriate noral curve for binomial probability $$\displaystyle{P}{\left({X}={6}\right)}$$