Historical data shows that 65% of students enrolled in a Math class at a local u

Question

Historical data shows that 65% of students enrolled in a Math class at a local university during any term pass the course. A randomly selected section of this course has 20 students enrolled. Answer the following questions based on this scenario. (Show the formula or the calculator command that you use as appropriate)

What type of probability distribution applies to this problem?

Identify the characteristics of this distribution by circling them in the list provided below:

It is a symmetric distribution.

There are a finite number of trials.

There are two outcomes for each trial.

The trials are dependent.

The probability of success remains constant.

The trials are independent.

Find the probability that exactly 15 students in this section will pass this term.

_________________________________________________________________________________

Find the probability that no more than 10 students pass the course this term.

_________________________________________________________________________________

Find the probability that at least 8 students pass the course.

__________________________________________________________________________________

Would it be unusual for exactly 17 students to pass the course this term? Justify your answer.

Find the expected number of students (i.e. the expected value of this probability distribution) and standard deviation of number of students who will pass the course this term.

____________________________________________________________________________________

Explanation / Answer

Binomial distribution should be used for this using the below formula:-

P(X=x,n,)=n!/x!(n-x)!* ^x*(1- )^n-x

a)      Find the probability that exactly 15 students in this section will pass this term.

0.1272

b) Find the probability that no more than 10 students pass the course this term.

0.1218

c) Find the probability that at least 8 students pass the course.

0.9940

d) Would it be unusual for exactly 17 students to pass the course this term? Justify your answer.

Yes it would be because in case 17 students pass, then in % terms it would be 85%

e) Find the expected number of students (i.e. the expected value of this probability distribution) and standard deviation of number of students who will pass the course this term.

µ=n=(20)(0.65)=13

S.D=sqrt(n(1-))

     =sqrt(20*0.65*0.35)

    =2.133

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