A multiple-choice quiz has 150 questions, each with 5 possible answers of which only 1 is correct. What is the probability that sheer guesswork yields from 30 to 35 correct answers for the 90 of the 150 problems about which the student has no knowledge

Step-by-step explanation:

From the data given;

A multiple-choice quiz has 150 questions

possible answers = 5

correct answer = 1

Let ; The probability of the correct answer = p

Probability of (p) = 1/5

= 0.20

we know that ;

p+q = 1

q = 1 - p

q = 1 - 0.20

q = 0.8

What is the probability that sheer guesswork yields from 30 to 35 correct answers for the 90 of the 150 problems about which the student has no knowledge

We can say that the number of guessed answer should be the sample size n = 90 ,

The probability of getting the correct answer to be  between 30 - 35

x = 30,31,32,33,34,35

Using a Binomial Distribution approach to solve this question; we have the formula:

Thus;

Thus; the probability that sheer guesswork yields from 30 to 35 correct answers for the 90 of the 150 problems about which the student has no knowledge is 0.00206

the expected value of the random variable : 0, 1 and 2

step-by-step explanation:

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq