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# X denotes a binomial random variable with parameters n and p. For each exercise, indicate

Binomial probability
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asked 2020-11-27

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.
$$\displaystyle{P}{\left({7}{<}{X}{<}{10}\right)}$$

## Answers (1)

2020-11-28

Step 1
Continuity correction:
The binomial probability is converted to a normal distribution probability by using the continuity correction.
Step 2
If the binomial probability represents “$$\displaystyle{a}{<}{X}{<}{b}$$” then add 0.5 to a and subtract 0.5 with b.
That is,
$$\displaystyle{P}{\left({7}{<}{X}{<}{10}\right)}={P}{\left({7}+{0.5}{<}{x}{<}{10}-{0.5}\right)}$$
$$\displaystyle={P}{\left({7.5}{<}{x}{<}{9.5}\right)}$$
Step 3
Thus, the area between 7.5 and 9.5 under the appropriate normal curve would estimate the binomial probability $$\displaystyle{P}{\left({7}{<}{X}{<}{10}\right)}$$.

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