Astate end-of-grade exam in american history is a multiple-choice test that has 50 questions with 4 answer choices for each question. a student must get at least 25 correct to pass the test, and the questions are very difficult. question 1. if a student guesses on every question, what is the probability the student will pass? (round your answer to 4 decimal places). question 2. suppose, after studying, a student raises her chances of getting each question correct to 0.70. what is the probability that she will pass? (round your answer to 4 decimal places).

Q1) The student has a 0.01% probability of passing the test.

Q2) She has a 99.91% probability of passing in the test.

Step-by-step explanation:

For each question, there are only two possible outcomes. Either he gets it correct, or he gets it wrong. So we solve this problem using the binomial probability distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinatios of x objects from a set of n elements, given by the following formula.

And is the probability of X happening.

For this problem, we have that:

Question 1.

There are 50 questions, so .

The student is going to guess each question, so he has a probability of getting it right.

He needs to get at least 25 question right.

So we need to find .

Using a binomial probability calculator, with and we get that .

This means that the student has a 0.01% probability of passing the test.

Question 2.

Now, we need to find with . So

She has a 99.91% probability of passing in the test.

walter needs to make at least 5 more cookies but no more than 40. 5 ≥ x ≥ 40;

step-by-step explanation:

walter has to make a minimum of 20 cookies. he already has 15 cookies made, so he must make 5 more to meet the minimum.

the maximum amount of cookies he can make is 55. he already has 15, so he has to make no more than 40 more cookies to meet the maximum.

12cm

the answer is d