Hey everybody I am having trouble with thisproblem: A test consists of 10 true/f

Question

Hey everybody I am having trouble with thisproblem:

A test consists of 10 true/false questions. Topass the test a student must answer at least 8 questionscorrectly.
a) If a student guesses on each question, what is the probabilitythat the student will pass the test?
b) Find the mean and standard deviation of the number of correctanswers.
c) It is unusual for a student to pass by guessing?Explain

I have the ANSWER a)0.0055     b) mean=5, Std Dev.=1.581  
c) the unusual # of correct answers is 2 to 8. So passing byguessing is not unusual.

But I need to know how do you get this. Please show all steps. Willgive a Lifesaver. Thanks

Explanation / Answer

a) This represents a binomial distribution with n=10 andp=.5 We want to know the probability that the number correct is 8, 9, or10. (10 choose 8)(.5)8(.5)2 + (10 choose9)(.5)9(.5) + (10 choose 10)(.5)10 = .055 b) The mean of a binomial distribution is np and the standarddeviation is (np(1-p)) In this case, the mean is 10(.5) = 5 and the standard deviation is((10)(.5)(.5)) = 1.581 c) To determine whether passing by guessing is "unusual", we willuse a 95% confidence interval. If a person guessingrandomly would fail greater than 95% of the time, we will call thisunusual. In this case, the person will not fail 95% of the timehowever. We determined in part A the 5.5% of the time theperson will pass the test by guessing. Passing by guessing istherefore not unusual

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