# Solving a Binomial Distribution Question

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Is this a binomial distribution question?

A student is taking a 10 question quiz. There are four possible answers to each question. The student decides to guess randomly on all 10 questions.

What is the probability the student will answer exactly six questions correctly?

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##### Solution Summary

The following problem helps with a statistics problem. This solution provides steps to answering a binomial distribution question. Step by step calculations are given for the solution.

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Q: Is this a binomial distribution question?

A: Yes, this is a binomial distribution question!

Let X be the number of questions the student answered correctly. Then X follows a binomial distribution with n=10, p=0.25 (Since the probability s/he guessed it correctly is 1/4=0.25).

So,

(1) the probability the student will answer exactly 6 questions correctly is

P(X=6)=C(10, ...

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"

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