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English Course - Probability - Exam, Exams of Probability and Statistics

Bharat Ratna Dr. B. R. Ambedkar UniversityProbability and Statistics

This is the Exam of Probability which includes Maximum, Hazard Rate Function, Continuous Random Variable, Density Function, Definition, Compute, Geometric, Geometric Random Variable etc. Key important points are: English Course, Certain University, Percentage, Students, Mutually Exclusive, Statistically Independent, Certain Restaurant, Toppings Available, Different Four Topping, Crispy Crust

Typology: Exams

2012/2013

Uploaded on 02/21/2013

rahull
rahull 🇮🇳

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Probability and Statistics Final Exam
Name:
Please show your work on all problems.
1. At a certain university, 60% of the students are enrolled in a math course, 50% are enrolled
in an English course, and 40% are enrolled in both. What percentage of the students are
enrolled in an English course and/or a math course?
2. Let Aand Bbe events such that P(A)=0.4and P(B)=0.3. Find P(A∪B)assuming
(a) Aand Bare mutually exclusive.
(b) Aand Bare statistically independent.
1
pf3
pf4
pf5

Partial preview of the text

Download English Course - Probability - Exam and more Exams Probability and Statistics in PDF only on Docsity!

Probability and Statistics Final Exam

Name:

Please show your work on all problems.

  1. At a certain university, 60% of the students are enrolled in a math course, 50% are enrolled in an English course, and 40% are enrolled in both. What percentage of the students are enrolled in an English course and/or a math course?
  2. Let A and B be events such that P (A) = 0. 4 and P (B) = 0. 3. Find P (A ∪ B) assuming

(a) A and B are mutually exclusive.

(b) A and B are statistically independent.

  1. Pizzas sold at a certain restaurant can be small, medium, or large, and they can have original crust or crispy crust. If there are eight toppings available, how many different four topping pizzas can be made? (The toppings are thoroughly mixed together before being applied to the pizza.)
  2. One in 2,000 people have a certain disease. There is a test for the disease that correctly diagnoses patients 99% of the time. In other words, the test is positive 99% of the time for patients with the disease, and it is negative 99% of the time for patients without the disease. If a randomly selected person tests positive for the disease, what is the chance he or she has the disease?
  1. On average, an automobile paint job has 2 flaws in a 10 ft^2 area. Find the probability that a 16 ft^2 area has at least one flaw. Assume that the flaws on the paint job form a Poisson process.
  2. A sample of radioactive material emits α-particles at an average rate of 4 per second accord- ing to a Poisson process.

(a) Let W be the waiting time in seconds until the first particle is emitted. Find the proba- bility density function for W.

(b) Let W 10 be the waiting time until the 10th^ α-particle is emitted. What type of distribu- tion does W 10 have? Find the expected value of W 10.

  1. At a doctor’s office, the time a patient waits between arriving and seeing a doctor is uni- formly distributed between 10 minutes and 25 minutes.

(a) Find the expected value of a patient’s waiting time.

(b) If a patient arrives at the doctor’s office at 4:00, find the probability that the patient sees a doctor before 4:17.

  1. Apples in a certain orchard have weights that are normally distributed with a mean of 120 grams and a standard deviation of 20 grams. Find the probability that a randomly selected apple weighs between 90 grams and 130 grams.