X denotes a binomial random variable with parameters n and p, Indicate which area under the appropriate normal curve would be determined to approximate the specified binomial probability. P(X >= 8)

alesterp 2021-02-24 Answered
X denotes a binomial random variable with parameters n and p, Indicate which area under the appropriate normal curve would be determined to approximate the specified binomial probability.
P(X8)
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Ezra Herbert
Answered 2021-02-25 Author has 99 answers

Step 1
Continuity correction:
The binomial probability is converted to a normal distribution probability by using the continuity correction.
If the binomial probability represents “\(\displaystyle{X}\ge{a}\)” then subtract 0.5 from a and 0.5 to n where n represents the number of trials.
Step 2
That is,
\(\displaystyle{P}{\left({X}\ge{8}\right)}={P}{\left({8}-{0.5}{<}{X}{<}{N}+{0.5}\right)}\)
\(\displaystyle={P}{\left({7.5}{<}{X}{<}{N}+{0.5}\right)}\)
Thus, the area between 7.5 and \(n+0.5\) under the appropriate normal curve would estimate the binomial probability \(\displaystyle{P}{\left({X}\ge{8}\right)}\).

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-05-21
At a certain college, 6% of all students come from outside the United States. Incoming students there are assigned at random to freshman dorms, where students live in residential clusters of 40 freshmen sharing a common lounge area. How many international students would you expect to find in a typical cluster? With what standard deviation?
asked 2022-02-12
What is P(x) for n=3, x=0, p=0.8?
asked 2021-09-19
Sue and Ann are taking the same English class but they do not study together, so whether one passes will be Independent of whether the other passes. In other words, "Sue passes and "Ann passes" are assumed to be independent events. The probebiity that Sue passes English is 0.8 and the probablity that Ann passes English is 0.75 What is the probability neither girl passes English?
asked 2022-02-11
If a binomial distribution applies with a sample size of n = 20, what is the probability of 5 successes if the probability of a success is 0.40?
asked 2021-09-21
Find the model of number of successful contacts from 1,000 sampled households.
asked 2022-03-03
In a 100 question true/false test what is the probability of getting 0 right answers? I'm struggling with formulas
asked 2022-03-12
A company prices its tornado insurance using the following assumptions:• In any calendar year, there can be at most one tornado.• In any calendar year, the probability of a tornado is 0.09.• The number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year.Using the company's assumptions, calculate the probability that there are fewer than 4 tornadoes in a 21-year period.