In Exercises, X denotes a binomial random variable with parameters

vazelinahS

vazelinahS

Answered question

2021-09-23

In Exercises, 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.
P(4<X<8)

Answer & Explanation

Dora

Dora

Skilled2021-09-24Added 98 answers

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,
\(\displaystyle{P}{\left({4}{<}{X}{<}{8}\right)}={P}{\left({4}+{0.5}{<}{x}{<}{8}-{0.5}\right)}\)
\(\displaystyle={P}{\left({4.5}{<}{x}{<}{7.5}\right)}\)
Step 3
Thus, the area between 4.5 and 7.5 under the appropriate normal curve would estimate the binomial probability \(\displaystyle{P}{\left({4}{<}{X}{<}{8}\right)}\).

Do you have a similar question?

Recalculate according to your conditions!

New Questions in High school probability

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?