I got the answers already and correct me if I am wrong. I just need help finding the mean and standard deviation for section B.
A quiz consists of 8 multiple choice questions, each with 5 possible answers.
a. If a student guesses on all 8 of the questions, do the number of questions
answered correctly form a binomial distribution?
A. Yes
b. If "yes", give the mean (µ) and standard deviation (σ), if "no" give at least 1
requirement of a binomial distribution that is not met.
I GOT : Yes it’s a binomial. p= 1/5=.2
yes
To determine if the number of questions answered correctly forms a binomial distribution, we need to check if the conditions for a binomial distribution are met. The conditions for a binomial distribution are:
1. The experiment consists of a fixed number of identical trials.
2. Each trial has only two possible outcomes - success or failure.
3. The probability of success (p) is constant for each trial.
4. The trials are independent of each other.
In the given scenario, a student is guessing on all 8 questions, with each question having 5 possible answers. This meets the conditions for a binomial distribution as follows:
1. The experiment consists of a fixed number of identical trials (8 questions).
2. Each trial has two possible outcomes - either the student answers correctly or incorrectly.
3. The probability of success (p) is constant for each trial, which is 1/5 or 0.2, as you correctly calculated.
4. The trials are independent of each other, as the outcome of one question does not affect the outcome of another.
Therefore, the number of questions answered correctly does form a binomial distribution.
Now, to calculate the mean (µ) and standard deviation (σ) for section B, we can use the formulas for a binomial distribution:
Mean (µ) = n * p
where n is the number of trials and p is the probability of success.
In this case, n = 8 (number of questions) and p = 0.2 (probability of answering correctly).
µ = 8 * 0.2 = 1.6
Standard Deviation (σ) = √(n * p * (1 - p))
σ = √(8 * 0.2 * 0.8) = √(1.28) = 1.13
Therefore, the mean (µ) for section B is 1.6 and the standard deviation (σ) is approximately 1.13.