Mathematics, 31.05.2020 05:57 uwauwa1234

Ms Davis is doing an activity with her statistic students where she gives them a 20 question multiple top choice test and they know none of the answers. Students need to guess on every question and each question has 5 possible choices, 1 of the which is correct.

What is the mean and standard deviation of the number of questions that each student gets correct?

Answers: 3

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Answer from: alyxkellar06

The mean will be "4" and the standard deviation will "1.789".

According to the question,

The probability of making 3 correct options will be:

→ $P(X) = \frac{1}{5}$

= 0.20

Total number of questions,

n = 20

As we know,

The mean will be:

→ $\mu = np$

By substituting the values, we get

$= 20\times 0.20$

= 4

and,

The standard deviation will be:

→ $\sigma = \sqrt{np(1-p)}$

$= \sqrt{20\times 0.20\times (1-0.20)}$

= 1.789

Thus the responses above are correct.

Learn more about standard deviation here:

link

Answer from: perezshayla56

The mean and standard deviation of the number of questions that each student gets correct are 4 and 1.789 respectively.

Step-by-step explanation:

Let the random variable X be defined as the number of correct answers marked by a student.

It is provided that each question has 5 possible choices, 1 of the which is correct.

Then the probability of marking thee correct option is:

$P(X)=\frac{1}{5}=0.20$

There are a total of n = 20 questions to be answered.

As the students does not the answer to any question, they would be guessing for each question. This implies that for a random question, all the five options has the equal probability of being correct and each of the five options can be correct independently from the other.

All these information above indicates that the random variable X follows a Binomial distribution with parameters n = 20 and p = 0.20.

The mean and standard deviation of a Binomial distribution are:

$\mu=np\\\\\sigma=\sqrt{np(1-p)}$

Compute the mean and standard deviation of the random variable X as follows:

$\mu=np=20\times 0.20=4\\\\\sigma=\sqrt{np(1-p)}=\sqrt{20\times 0.20\times(1-0.20)}=1.789$

Thus, the mean and standard deviation of the number of questions that each student gets correct are 4 and 1.789 respectively.

Answer from: Quest

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Answer from: Quest

step-by-step explanation:

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Ms Davis is doing an activity with her statistic students where she gives them a 20 question multipl...