Exam 2 2013
Exam 2 - Math 3200
Spring 2013
Name :
ID :
General instructions: This exam has 13 questions, each worth the same amount. Check that no pages are missing and promptly notify one of the proctors if you notice any problems with your copy of the exam. Mark your ID number on the six blank lines on the top of your answer card using one line for each digit. Print your name on the top of the card. Choose the answer closest to the solution and mark your answer card with a PENCIL by shading in the correct box. You may use a 4× 6 card with notes and any calculator that does not have graphing functions. GOOD LUCK!
1. An office supply warehouse receives an order for three computers. The warehouse has 50 computers in stock, two of which are defective. The order is filled by randomly drawing from the computers in stock. Let X be the number of defective computers in the order. What probability distribution describes P (X = x)?
(A) Gamma
(B) Uniform
(C) Geometric
(D) Bernoulli
(E) Binomial
(F) Exponential
(G) Poisson
(H) Hypergeometric
(I) Beta
(J) Normal
Solution: This is a hypergeometric distribution:
P (X = x) =
2 x 48
3−x
50
3
.
2. (Continuation of the previous problem.) Assume the same information given in problem 1. What is the probability P (X = 1)?
(A) 0.920
(B) 0.713
(C) 0.545
(D) 0.432
(E) 0.316
(F) 0.115
(G) 0.089
(H) 0.055
(I) 0.032
(J) 0.012
Solution:
P (X = 1) =
2
1
48
2
50
3
=
2 × 48×47
2
2
50×49×48
3×2
=
141
= 0.1151.
1225
3. A car travels between two cities A and C which are 75 miles apart. If the car has a breakdown, the distance X from the breakdown to city A is distributed as U [0, 75]. The driver is a member of an automobile service that has contracts with garages in cities A, B , and C , where city B is between cities
A and C , 25 miles from city A. If the car breaks down, it is towed to the closest garage. Find the probability that the car is towed more
Spring 2013
Name :
ID :
General instructions: This exam has 13 questions, each worth the same amount. Check that no pages are missing and promptly notify one of the proctors if you notice any problems with your copy of the exam. Mark your ID number on the six blank lines on the top of your answer card using one line for each digit. Print your name on the top of the card. Choose the answer closest to the solution and mark your answer card with a PENCIL by shading in the correct box. You may use a 4× 6 card with notes and any calculator that does not have graphing functions. GOOD LUCK!
1. An office supply warehouse receives an order for three computers. The warehouse has 50 computers in stock, two of which are defective. The order is filled by randomly drawing from the computers in stock. Let X be the number of defective computers in the order. What probability distribution describes P (X = x)?
(A) Gamma
(B) Uniform
(C) Geometric
(D) Bernoulli
(E) Binomial
(F) Exponential
(G) Poisson
(H) Hypergeometric
(I) Beta
(J) Normal
Solution: This is a hypergeometric distribution:
P (X = x) =
2 x 48
3−x
50
3
.
2. (Continuation of the previous problem.) Assume the same information given in problem 1. What is the probability P (X = 1)?
(A) 0.920
(B) 0.713
(C) 0.545
(D) 0.432
(E) 0.316
(F) 0.115
(G) 0.089
(H) 0.055
(I) 0.032
(J) 0.012
Solution:
P (X = 1) =
2
1
48
2
50
3
=
2 × 48×47
2
2
50×49×48
3×2
=
141
= 0.1151.
1225
3. A car travels between two cities A and C which are 75 miles apart. If the car has a breakdown, the distance X from the breakdown to city A is distributed as U [0, 75]. The driver is a member of an automobile service that has contracts with garages in cities A, B , and C , where city B is between cities
A and C , 25 miles from city A. If the car breaks down, it is towed to the closest garage. Find the probability that the car is towed more