Suppose that 70% of the students at a certain college live off-campus. In a clas

Question

Suppose that 70% of the students at a certain college live off-campus. In a class with 15 students, suppose each student lives off-campus with probability p = 0.7, independently of the others. Let X be the number of these students that live off-campus. a. Identify a suitable distribution to model X. b. What is the probability that at most 5 of these students live off-campus? c. What is the probability that at least 10 of these students live off-campus? d. How many students in this class are expected to live off-campus? e. Find the standard deviation of X. f. What is the probability that at least one of these students does not live off-campus?

Explanation / Answer

a) Let x be the number of student who live off-campus.

we use here Binomial distribution with n=15 and p=0.7

b)p(X<=5)=0.003653 .............................>>Using '=BINOMDIST(5,15,0.7,1)' in excel

c)P(X>=10)=1-P(X<10

=1-P(X<=9)

=1-0.2784 ..............................>> using '=BINOMDIST(9,15,0.7,1)' in excel

=0.7216

d) Expected value =E(x) =n*p=15*0.7 =10.5

Hope this will help you! Good Luck :)   

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