# Thread: Confidence Intervals and such

1. ## Confidence Intervals and such

Thank you in advance for any help!

1. The waiting time (in minutes) for a CATA bus at MSU is distributed
uniformly between θ - 3 and θ + 3. A sample of 75 students are taken and
their waiting times recorded.

a) Find V ( X-bar )
ATTEMPT: V(X) = 36/12 = 3
V(X-bar) = V(X)/n = 3/75 = .04

b) Find the 95% confidence interval for θ based on X-bar.
ATTEMPT: X-bar +/- Z(alpha/2) * sigma/sqrt(n)
= x-bar +/- 1.96 * 1.73/sqrt(75)
= x-bar +/- 0.392

c) Suppose θ = 3. Find the approximate value of the probability that the
waiting time of a randomly selected student exceeds 2.8 minutes.
ATTEMPT: P(Z ≤ (X - E(X))/sqrt(sigma^2/n))
P(X > 2.8) = 1 - P( Z ≤ (2.8-3.0)/sqrt(3.0/75))
= 1 - P( Z ≤ -1.0 )
= 1 - .1587 = .8413

2. ## Re: Confidence Intervals and such

Updated:
I've had one person try to help me solve this problem and they found V(X) to be (9^2)/12 = 6.75. I'm quite sure it's (6^2)/12 as the thetas cancel out leaving us with ((3+3)^2)/12 = 3. That would mean V(X-bar) is 3/75 = .04.

I'm not quite sure if the other two parts are right either.