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ayoismeisalex
19.08.2020 •
Mathematics
A quiz consists of 15 multiple choice questions, each with five possible answers, only one of which is correct. If a student guesses on each question, what is the mean and standard deviation of the number of correct answers
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Ответ:
The mean and standard deviation of the number of correct answers is 3 and 1.55 respectively.
Step-by-step explanation:
We are given that a quiz consists of 15 multiple choice questions, each with five possible answers, only one of which is correct.
Let X = the number of correct answers
The above situation can be represented through binomial distribution;
where, n = number of samples (trials) taken = 15 multiple choice questions
r = number of success
p = probability of success which in our question is probability of
one correct answer out of 5, i.e; p =
= 0.2
So, X ~ Binom(n = 15, p = 0.2)
Now, the mean of the number of correct answers is given by;
Mean of X, E(X) =![n \times p](/tpl/images/0724/4265/3194b.png)
=
= 3
And the standard deviation of the number of correct answers is given by;
Standard deviation, S.D.(X) =![\sqrt{n \times p\times (1-p)}](/tpl/images/0724/4265/74f69.png)
=
= 1.55
Ответ:
It seems like the holding tanks combine to make a cylinder, so we use pir^2h to multiply it out and get π(30)^2(110)= around 311018 total, and 155509 each