# Let X represent the number of times your professor goes to the gym each week. You are given the

Question

Carleton University

School of Mathematics and Statistics

STAT 2606 – Assignment #3 – Fall 2015

1. Let X represent the number of times your professor goes to the gym each week. You are given the following probability table for X. Unfortunately, your professor spilled some coffee on the probability for x = 5 and it is now illegible.

x12345 P(X = x) 0.12 0.25 0.38 0.17 ???

(a) What is P(X = 5)?

(b) Find the expected value of X. (c) Find the standard deviation of X.

2. Suppose the number of mechanical failures occurring in an industrial plant follows a Poisson distribution with an average of 1.4 failures per week.

(a) What is the probability of no mechanical failures in a given week?

(b) What is the probability that four or more mechanical failures will occur during a three-week period?

3. A student is preparing for an upcoming midterm exam. The professor given the student 40 practice questions and plans to select 12 of the questions at random to create the midterm exam. Suppose the student knows how to correctly answer 34 of the 40 questions. Let X represent the number of questions the student answers correctly on the exam.

(a) What is the probability distribution of X?

(b) What is the probability that the student will know how to answer at least 10 questions on the exam?

4. Jed Clampett, the president of Ozark Oil, plans to conduct a preliminary survey to locate oil deposits. The probability of striking oil at a single location is 0.15, independent of all other locations.

(a) If Jed decides to drill for oil at 20 different locations, what is the probability that he will strike oil at 3 or more of those locations?

(b) If Jed decides to drill for oil at 200 locations, approximate the probability that he will strike oil at 30 or more of these locations. Justify any approximation procedure that you use.

5. Suppose the weights of packages of Oreo cookies have a normal distribution with a mean of 252 grams and a standard deviation of 9 grams.

(a) What proportion of all packages weigh between 245 grams and 265grams? (b) What proportion of all packages weigh more than 260 grams?

(c) What weight should be advertised on the packages so that only 10% of packages fall below the advertised weight?

6. Suppose that the waiting time to be served at a “drive thru” follows an exponential distribution with a mean of 3.2 minutes.

(a) What is the probability a randomly chosen customer will wait more than 5 minutes to be served? (b) Find a time such that 90% of all customers are served within that time.

7. Let X ~ B(20, 0.65).

(a) Use MINITAB to print the cumulative probability table for X.

(b) Use the output from part (a) to calculate each of the following probabilities:

(i) P(X ?14) (ii) P(X < 14) (iii) P(X ?14) (iv) P(10? X ?16)

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