The survey by the National Center for Health Statistics further found that 49% o

Question

The survey by the National Center for Health Statistics further found that 49% ofadults ages 25-29 had cell phone and no landline. We randomly select four 25-29-year-olds. 9· a What is the probability that all of these adults have only a cell phone and no landline? b. What is the probability that none of these adults have only a cellphone and no landline? c. What is the probability that at least one of these adults has only a cell phone and no landline? In a large Introductory Statistics lecture hall, the professor reports that 55% of the students enrolled have never taken a Calculus course, 32% have taken only one semester of Calculus, and the rest have taken two or more semesters of Calculus. The professor randomly assigns students to groups of three to work on a project for the course. What is the probability that the first groupmate you meet has studied: io a. two or more semesters of Calculus? b. some Calculus? c. no more than one semester of Calculus?

Explanation / Answer

pmf of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
where
k = number of successes in trials   
n = is the number of independent trials   
p = probability of success on each trial
I.
mean = np
where
n = total number of repetitions experiment is excueted
p = success probability
mean = 4 * 0.49
= 1.96
II.
variance = npq
where
n = total number of repetitions experiment is excueted
p = success probability
q = failure probability
variance = 4 * 0.49 * 0.51
= 0.9996
III.
standard deviation = sqrt( variance ) = sqrt(0.9996)
=0.9998
9.A
P( X = 4 ) = ( 4 4 ) * ( 0.49^4) * ( 1 - 0.49 )^0
= 0.0576
9.B
P( X = 0 ) = ( 4 0 ) * ( 0.49^0) * ( 1 - 0.49 )^4
= 0.0677
9.C
P( X < 1) = P(X=0)   
= ( 4 0 ) * 0.49^0 * ( 1- 0.49 ) ^4
= 0.0677
P( X > = 1 ) = 1 - P( X < 1) = 0.9323

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