AMS 315, Examination I Summer II

Exam > AMS 315, Examination I Summer II

Stony Brook University AMS 315 The examination contains 6 problems. This examination is worth 250 points. Work each problem on the scratch papers. Please write your name and ID on every page. You may use a calculator without programming or graph functions. Computers and cellphones are not allowed to use in this exam. You may also use a single sheet ...[Show More]

Stony Brook University
AMS 315
The examination contains 6 problems. This examination is worth 250 points. Work each

problem on the scratch papers. Please write your name and ID on every page. You may

use a calculator without programming or graph functions. Computers and cellphones

are not allowed to use in this exam. You may also use a single sheet of notes in your

handwriting that is the size of the paper in this examination. You are on your honor not

to use any other assistance during this examination. Turn in both your scratch papers

and your notes at the end of the examination.

1. When it snows over 1 foot, there is a 80% chance of class being cancelled.

When it does not snow over 1 foot, there is only a 10% chance of class being

cancelled. The forecast shows an 90% chance that there will be over 1 foot of

snow tomorrow.

(a) (10 points) What is the probability that class is cancelled tomorrow?

(b) (5 points) Find the probability that it snows over 1 foot, given that class is

cancelled tomorrow.

2. A certain bridge will collapse under a weight that exceeds 300,000 pounds.

Suppose the weight of cars has a mean of 2,800 pounds with a standard deviation

of 800. What is the probability that holding 100 cars will cause the bridge to

collapse? (15 points)

3. A research team conducted a pilot study of whether a training program

improved the productivity of a firm's workers. They took a random sample of n=3

workers and measured their productivity Y before and after the training program.

The average productivity increase was 𝑦̅3 = 5.66 units, and the sample variance of

the productivity increase was 16.7 (the divisor in the variance was n-1).

(a) (5 points) Prove the sample mean 𝑋̅ = 𝑋1+𝑋2+⋯+𝑋𝑛

𝑛

is an unbiased estimator

for E(X), n is some positive integer