Question

In: Statistics and Probability

Assume that random guesses are made for six multiple choice questions on an SAT​ test, so...

Assume that random guesses are made for six multiple choice questions on an SAT​ test, so that there are n equals 6 ​trials, each with probability of success​ (correct) given by p equals 0.6. Find the indicated probability for the number of correct answers. Find the probability that the number x of correct answers is fewer than 4. Upper P left parenthesis Upper X less than 4 right parenthesis equals nothing ​(Round to four decimal places as​ needed.)

Solutions

Expert Solution

Let , X be the number of correct answers.

Here ,

The pmf of X is ,

; x=0,1,2,.....,n and q=1-p

= 0 ; otherwise

Therefore, the indicated probability distribution table is ,

X P(X=x)
0 1 1 0.004096 0.0041
1 6 0.6 0.01024 0.0369
2 15 0.36 0.0256 0.1382
3 20 0.216 0.064 0.2765
4 15 0.1296 0.16 0.311
5 6 0.07776 0.4 0.1866
6 1 0.046656 1 0.0467

Now ,

P(X<4)=P(X=4)+P(X=3)+P(X=2)+P(X=1)+P(X=0)

=0.3110+0.2765+0.1382+0.0369+0.0041

=0.7667

Therefore , the probability that the number x of correct answers is fewer than 4 is 0.7667.


Related Solutions

Assume that random guesses are made for ninenine multiple choice questions on an SAT​ test, so...
Assume that random guesses are made for ninenine multiple choice questions on an SAT​ test, so that there are nequals=99 ​trials, each with probability of success​ (correct) given by pequals=0.450.45. Find the indicated probability for the number of correct answers. Find the probability that the number x of correct answers is fewer than P(X<4)=
Assume that random guesses are made for seven multiple choice questions on an SAT​ test, so...
Assume that random guesses are made for seven multiple choice questions on an SAT​ test, so that there are equals ​trials, each with probability of success​ (correct) given by p =0.45 . Find the indicated probability for the number of correct answers. Find the probability that the number x of correct answers is fewer than 4 .
assume that random guesses are made for eight multiple choice questions on a SAT test so...
assume that random guesses are made for eight multiple choice questions on a SAT test so that there are n=8 trials, each with probability of success (correct) given by p=0.20 a) prob of number x of correct answers is exactly 7 b) prob of numer x correct answers is at 4 c) prob of number x correct answers is fewer than 3 d) prob of number x corrwct answers is no more than 2 e) prob of no correct answers
assume that random guesses are made for 7 multiple choice questions test, with 5 choices for...
assume that random guesses are made for 7 multiple choice questions test, with 5 choices for each questions, so that there are n=7 trials, each with probability of success (correct) given by p=0.20 Find the probability of not correct answers
3) Binomial Probabilities. Assume random guesses are made for eight multiple choice questions, each with p...
3) Binomial Probabilities. Assume random guesses are made for eight multiple choice questions, each with p = .20 probability of guessing the correct answer. Round probabilities to 3 decimal places. A.) Find the probability of guessing all of them correctly. B.) Find the probability of getting exactly three correct. C.) Find the probability of getting them all wrong. D.) Find the probability that at least one is wrong.
If you make random guesses for 10 multiple choice test questions each with 5 possible answers),...
If you make random guesses for 10 multiple choice test questions each with 5 possible answers), what is the probability of getting all answers correct?
An SAT test has 8 questions, each question having 5 multiple choice answers. If a student...
An SAT test has 8 questions, each question having 5 multiple choice answers. If a student make random guesses for each answer, find the probability that: a)the number of correct answers is 7. b)the number of correct answers is at least 4. c)the number of correct answers is fewer than 3.
A multiple choice test consists of 8 items each with 4 choices. A student guesses the...
A multiple choice test consists of 8 items each with 4 choices. A student guesses the answers by choosing an answer at random. Compute the probability that (a) the student answers all questions incorrectly? (b) the student answers all questions correctly? (c) the student answers 2 or more correctly? (d) Suppose the student is able to eliminate one of the answers as incorrect and chooses randomly from the other three choices. What is the probability the student answers 2 or...
quiz has 5 questions. multiple choice with 4 possible answers each. a student randomly guesses on...
quiz has 5 questions. multiple choice with 4 possible answers each. a student randomly guesses on all 5 questions. 1) what is the probability of that student getting a passing grade(60% correct is passing) 2) what is the probability of that student getting a B or better (a low B is 80%) 3) what is the probability of that student failing the quiz?
The results of a (20 questions) multiple choice questions exam are recorded. Random samples of 10...
The results of a (20 questions) multiple choice questions exam are recorded. Random samples of 10 and 12 students are investigated. For the 10 student sample, the individual performances are 11, 8, 8, 3, 7, 5, 9, 5, 1, and 3 errors. For the 12 student sample, the individual performances are 10, 11, 9, 7, 2, 11, 12, 3, 6, 7, 8, and 12 errors. Assuming the population standard deviations are equal, use the 0.10 level of significance in testing...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT