Autumn 2012 ST370 Version BETA QUIZ 2 Dr. C. E. Smith, 1.5 hour, 1 sheet notes, ok calculator&tables

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1 Autumn 01 ST370 Version BETA QUIZ Dr. C. E. Smith, 1.5 hour, 1 sheet notes, ok calculator&tables NAME ID # I will neither give nor receive help from other students during this quiz Sign PROBLEMS 1 & : Suppose E[ Let Y = 3 ] = 5 and E[ 4 and ] = and with variances Var[ Problem 1: Find the mean or expected value of Y a) 0 b) 7 c) 3 d) 31 e) 59 Problem : Find the variance of Y are INDEPENDENT random variables with means of ] = 3 and Var[ a) -31 b) -133 c) 187 d) 49 e) none of these 1 ] = 10 Problem 3: A nerf basketball shooter is shooting from a distance where he is a 15 % shooter, that is he makes 15% of his shots. If he shoots 10 shots, what is the VARIANCE of the number of shots he makes? A B) 1.5 C) (1.5) D E PROBLEM 4:. Suppose that X has a Weibull cumulative distribution function F(t) = 1 - exp(- ) for t > 0. ( t) What is Pr( t <.50)? (to 4 decimals) A B..631 C D E. None of the above PROBLEM 5: Recall that a density function for a continuous random variable is the derivative of the cumulative distribution function. What is the density function of X in the previous problem? A. B. C. 8t 16t 4t D. 8t E. None of the above

2 Problem 6: Suppose that A and B are events with P(A) = 0.04 and P(B) = P(A B) = 0.00, find P(A or B) = a) b) c).089 d).0871 e) Problem 7: A quality-control inspector is testing sample output from a production process for widgets wherein 98% of the items are satisfactory (S) and % are unsatisfactory (U). Three widgets are chosen randomly for inspection. The successive quality events may be assumed independent. Find the probability for obtaining EXACTLY ONE of satisfactory items: a) b) c) d).0675 e) none of these Problem 8 : The table below shows the number of students that fall into each of several categories. One student will be selected at random in a raffle, and will be given a new laptop with a WOLFPACK screensaver on it. FEMALE CIVIL ELECTRICAL MECHANICAL TEXTILE MALE Find the following conditional probability: Pr[ male not a mechanical engineer ] = a) 8/13 b) 5 /13 c) 1/3 d) 13/ 4 e) none of these Problem 9: A system has the following SIX independent components with reliabilities of FIVE of them written within the component boxes. The reliability of the system (to three decimal places) is : FIND THE VALUE OF THE MYSTERY COMPONENT DENOTED BY?? R1= R4= R= ?? R5= R3= a).976 b).9683 c).7488 d).865 e) no such component exists

3 Problem 10: A computer time-sharing system receives teleport inquiries at an average rate of.1 per millisecond. Find the probability that the number of inquiries in a particular 50-millisecond stretch will be equal to 5 a) b).76 c).3840 d).57 e).1755 Problem 11: The probability distribution for the number of defective items in a random sample is as follows: x p(x) Find the Expected value of X a) 1.0 b).13 c) 3.68 d) 1.94 e).5 Problem 1: For the random variable having the following probability density function, f(x)=1/6 for all 0 < x < 6 and 0 otherwise determine Pr(0.7 < x < 1.7) a).0700 b).0833 c).1667 d).3333 e) Problem 13: Determine the value for the constant k that will make the function below a probability density function. f(x) = k x^4, for x in (0,), and f(x) = 0, for all other x.; k = a) /7 b) 8/3 c) 3/8 d) 3/64 e) none of these Problem 14: At a local circus, Terrific Tomoko tames tumultuous tigers. Assume the time it takes her to tame a tiger has an exponential probability density with a mean of days. What is the probability that the next tiger tamed with take AT LEAST days? a) b).631 c).0183 d).9817 e) none of these Problem 15: In a dice-tossing random experiment, a Red die and a Green die are thrown independently. Consider as a random variable, X, the range in showing dots (that is the largest value-smallest value). For example if the red die is 6 and the green die is 4, then the random variable has a value of in that experiment. Calculate the probability, Pr(X=) = a).111 b).0556 c).78 d). e).167 3

4 Problem 16: A student selects his answers on a true/false examination by tossing a coin (so that any particular answer has a.50 probability of being correct). He must answer at least 70% correctly in order to pass. Find his probability of passing when the number of questions on the quiz is 10 a).0547 b).0577 c).9453 d).9793 e).1719 Problem 17 : Customers are RANDOMLY ASSIGNED as they make appointments at the Chapel College Dental Health Clinic. They are assigned to Dentist Sally with probability 0.3 Dentist Theresa with probability 0.5 And Dentist Nathan with probability 0. The clinic only has two Hygenists: Yuri and Cameron. IF dentist Sally is chosen, THEN hygienist Yuri is assigned with probability 1/3 And hygienist Cameron with probability /3. IF dentist Theresa is chosen, THEN hygienist Yuri is assigned with probability 3/5 And hygienist Cameron with probability /5 IF dentist Nathan is chosen, THEN hygienist Yuri is assigned with probability 0 And hygienist Cameron is assigned with probability 1. (HINT: draw a probability tree) GIVEN that the customer ended up with hygienist Yuri, What is the probability they were assigned dentist Sally? a) 0.10 b).3333 c).5 d).30 e) none of these PROBLEM 18: : The elongation of a steel bar under a particular tensile load may be assumed to be normally distributed, with a mean of.06 in. and standard deviation of.008 in. A sample of n=100 bars is subjected to the test. Find the probability that the sample mean elongation is between.059 in. and.061 in. a).8944 b) c).0956 d).1034 e) none of these PROBLEMS 19 and 0 : The average active-ingredient yield per liter of raw material for samples of vials may be approximated by a normal distribution with mean 4 grams and variance of 4 grams^. Problem 19: Find: Pr[average yield of a sample is more than 3.66 grams] a).407 b).435 c).4681 d).5675 e) none of these Problem 0: the 99 th percentile for the yield is a) 8.66 b).57 c).33 d) 33.3 e) none of these 4

5 5 point EXTRA CREDIT: What was your biggest problem in completing your course project, e.g. data entry, ANOVA, etc.? Formulas that could be of use: ( n) ( n 1)! integral n1 n x x dx n 1 The binomial(n; π) probability mass function is n! k n k Pr(X = k) = (1 ) k! n k! k = 0, 1,, n The Poisson probability mass function for mean process rate and time span t is Pr(X = k) = k = 0, 1,, k ( t) e k! t 5

(a).40 (b).05 (c).20 (d).10 (e) none of these

(a).40 (b).05 (c).20 (d).10 (e) none of these STT 421 Some Example Multiple Choice Questions October 24, 2016 Correction to Answer for Prob 50 November 1, 2016 1. Here are the ages for children in a population of 5 children: {2, 2, 4, 5, 7}. An SRS