Ask question

Ask question

All categories

3 years ago

5

A multiple choice exam has 20 questions. Each question has 3 possible answers; there is no partial credit. Only 1 answer out of

the 3 possible answers is correct; no questions are dependent on getting the correct answer for a previous question. The passing score for the exam is 60% or better. If you randomly guess the answer to each question, what is the probability that you will pass the test? Round your answer to three decimal places and report as a DECIMAL - example: 0.234

1 answer:

amid [387]3 years ago

6 0

Answer:To find out the theoretical probability of the case given, we need to make certain assumptions.

First, we'll assume that he'll attempt all of the questions, i.e he'll attempt all 10 questions.

Next assumption is that each option in each question is equally likely to be marked by the student.

This pretty much leads us to a binomial probability distribution.

Conditions are:

Answers 10 questions.

Each question has 4 options with only one correct answer and all other incorrect answers.

Student is equally likely to pick any outcome in any given question.

Hence, probability of choosing correct answer is 1/4 = 0.25. Probability of choosing incorrect answer is 1–1/4 = 3/4 = 0.75.

The number of trials is 10.

Total number of success is exactly 8 and failure is 2 amongst the 10 questions in any particular order.

Now, calculation is fairly simple.

Binomial probability distribution is such that…

P(8 correct ; 2 wrong)

= 10C8 × (0.25)^8 × (0.75)²

= 405/1048576 ≈ 3.862380981 × 10^-4 ≈ 0.000386

Step-by-step explanation:

You might be interested in

A rectangular field with one side along a river is to be fenced. Suppose that no fence is needed along the river, the fence on t

Andreas93 [3]

Answer:

a) Side Parallel to the river: 200 ft

b) Each of the other sides: 400 ft

Step-by-step explanation:

Let L represent side parallel to the river and W represent width of fence.

The required fencing (F) would be $F=L+2W$ .

We have been given that field must contain 80,000 square feet. This means area of field must be equal to 80,000.

$LW=80,000...(1)$

We are told that the fence on the side opposite the river costs $20 per foot, and the fence on the other sides costs $5 per foot, so total cost (C) of fencing would be $C=20L+5(2W)\Rightarrow 20L+10W$ .

From equation (1), we will get:

$L=\frac{80,000}{W}$

Upon substituting this value in cost equation, we will get:

$C=20(\frac{80,000}{W})+10W$

$C=\frac{1600,000}{W}+10W$

$C=1600,000W^{-1}+10W$

To minimize the cost, we need to find critical points of the the derivative of cost function as:

$C'=-1600,000W^{-2}+10$

$-1600,000W^{-2}+10=0$

$-1600,000W^{-2}=-10$

$-\frac{1600,000}{W^2}=-10$

$-10W^2=-1,600,000$

$W^2=160,000$

$\sqrt{W^2}=\pm\sqrt{160,000}$

$W=\pm 400$

Since width cannot be negative, therefore, the width of the fencing would be 400 feet.

Now, we will find the 2nd derivative as:

$C''=-2(-1600,000)W^{-3}$

$C''=3200,000W^{-3}$

$C''=\frac{3200,000}{W^3}$

Now, we will substitute $W=400$ in 2nd derivative as:

$C''(400)=\frac{3200,000}{400^3}=\frac{3200,000}{64000000}=0.05$

Since 2nd derivative is positive at $W=400$ , therefore, width of 400 ft of the fencing will minimize the cost.

Upon substituting $W=400$ in $L=\frac{80,000}{W}$ , we will get:

$L=\frac{80,000}{400}\\\\L=200$

Therefore, the side parallel to the river will be 200 feet.

4 0

3 years ago

Solve for the unknown angle

Helga [31]

Answer:

30

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Tyler orders a meal that costs $15.

olganol [36]

The answer is 69 dollars and the titian would be 69 dollas

6 0

3 years ago

A jar contains 4 blue marbles, 6 red marbles, 10 purple marbles, and 5 green marbles. If you choose one marble, what is the prob

Paladinen [302]

It be a 3/4 possibility that it won’t be green

6 0

3 years ago

Please help with this SAT question. A solution gets Brainliest!

baherus [9]

Answer:

<h2>i think C</h2>

hope its help

C is my answer

3 0

2 years ago