a. None have E-Z pass?

b. All have E-Z pass?

c. All but 2 have E-Z pass?

d. At least 2 have E-Z pass?

Tutors, sign in to answer this question.

Ryan S. | Mathematics and StatisticsMathematics and Statistics

This is a binomial distribution problem. I highly recommend researching this distribution online or in your textbook. Here is the pmf. P(N=n) = p(n) = k C n q^n*(1-q)^(k-n) where k is the total number of "trials," n is the number of "successes," and q is the probability of success in a single trial. k C n is the number of combinations of n objects chosen from k objects. In this problem the trials are the cars at the toll booth, k = 5, q=0.68.

a) n= 0 p(0) = (5 C 0)*0.68^0*0.32^5=0.0034

b) n= 5 p(5) = (5 C 5)*0.68^5*0.32^0=0.1454

c) n= 3 p(3) = (5 C 3)*0.68^3*0.32^2=0.3220

d) n= 2, 3, 4, or 5 We can get this from n is not 0 or 1 or 1-p(0)-p(1). We already have p(0)=0.0034

p(1)= (5 C 1)*0.68^1*0.32^4=0.0357

so the answer is 1-.0034-.0357=.9609

You will need the binomial distribution B(5,0.68;k) with probabilities P=C(5,k)*0.68

a) k=0, P=C(5,0)*0.68

If you have a statistics calculator like the TI-84, use the function binomialpdf(5,0.68,0).

b) k=5, use binomialpdf(5,0.68,5), get P=C(5,5)*0.680^{5}*0.32^{0}=0.145

c) k=3, use binomialpdf(5,0.68,3), get P=0.322

d) k≥2, P(k≥2)=1-P(k<2)=1-0.039=0.961

On the TI-84, use 1-binomialcdf(5,0.68,1). (This is the cumulative distribution, it adds up

all values 0..k.)

all values 0..k.)

a) (1-.68)^5 = .32^5

b) .68^5

c) 5C2 (.68)^2 (.32)^3, binomial probability

d) 1 - ∑{i=0,1)5Ci (.68)^(5-i) (.32)^i, using complement set

Given P(a) = 68%

P(/a) = 1 - P(a) = 1-0.68 = 32%

P(b) = 1 x P(a) = 68%

P(c) = P(a) x (1-P(/c)) = 40.8%

P(d) = P(a) x (1-P(/d)) = 27.2%

Already have an account? Log in

By signing up, I agree to Wyzant’s terms of use and privacy policy.

Or

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Your Facebook email address is associated with a Wyzant tutor account. Please use a different email address to create a new student account.

Good news! It looks like you already have an account registered with the email address **you provided**.

It looks like this is your first time here. Welcome!

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Please try again, our system had a problem processing your request.

Harry O.

Harry O: tutoring in ACT, algebra, geometry, physics and calculus

$12.50 per 15 min

View Profile >

Michael B.

Seasoned Math Tutor, and U.S. History/Politics Expert

$10 per 15 min

View Profile >

Robyn N.

Experienced and Friendly Math Tutor

$10 per 15 min

View Profile >

## Comments