SMAM Exam 1 Name

Transcription

1 SMAM Exam 1 Name 1. A chemical reaction was run several times using a catalyst to control the yield of an undesireable side product. Results in units of percentage yield are given for 24 runs A. Complete the stem and leaf display.(5 points) B. Make a five number summary. (5 points) First five # summary by Tukey method. Using the book s method or the calculator will give you the same result for the quartiles in this particular case.second summary computes quartiles by Minitab s method.

2 C. Find the interquartile range and determine whether there are any outliers and find them. (5 points) Based on l values IQR = = xIQR = is outlier Based on second five # summary IQR = = x IQR = Using this five number summary there are no outliers. D. Draw a boxplot.(5 points) Based on first five number summary Based on second five number summary. 7 Boxplot of C1 6 2C

3 2. A. A chemical engineer is designing an experiment to determine the effect of temperature, stirring rate and type of catalyst on the yield of a certain reaction. She wants to study five different reaction temperatures, two different stirring rates and four different catalysts. If each run of the experiment involves a choice of one temperature, one stirring rate and one catalyst how many experimental runs are possible?(5 points) 5x2x4 =40 B. A company has hired 15 new employees and must assign 6 to the day shift, 5 to the graveyard shift and 4 to the night shift. In how many ways can the assignment be made? (5 points) 15! 6!5!4! = C. A lot has 20 bolts four of which are defective. If five bolts are drawn from the lot without replacement what is the probability of obtaining 2 good bolts and 3 defective bolts?(5 points) = = The probability that a car will come to a full stop at a stop sign is 0.4. A. Suppose that 10 cars are observed. What is the probability that (1) Exactly two cars come to a full stop? (4 points) P[X = 2] = P[X 2] P[X 1] = =.1209 (2) At least two cars come to a full stop?(4 points) P(X 2) = 1 P(X 1) = =.9536 B. Suppose that cars are observed until a certain number of them come to a full stop? What is the probability that (1) At most four cars are observed until one comes to a full stop?(4 points) P(Y 4) = (0.6)(0.4) + (0.6) 2 (0.4) + (0.6) 3 (0.4) =.8704

4 (2) Exactly four cars are observed until two come to a full stop?(4 points) P[Y = 4] = 3 1 (.4)2 (.6) 2 = A lot of 15 items has three defectives. A quality control inspector inspects four items chosen at random and if they are good accepts the lot. What is the probability that the lot is rejected?(10 points) P(reject) = 1 P(accept) = = = The number of flaws in a certain type of lumber follows a Poisson distribution with a rate of 0.5 per linear meter. A. What is the probability that a one meter board has at least one flaw?(5 points) P(X 1) = 1 e.5 = =.393 B. What is the probability that a two meter board has exactly two flaws?(5 points) P[X = 2] = 12 e 1 = !

5 C. How long must a board be so that the probability it has no flaw is 0.5?(5 points) e.5l =.5.5L = ln(.5) = ln 2 L = 2ln 2 = A chemical supply company ships a certain solvent in 10-gallon drums. Let X represent the number of drums ordered by a randomly selected customer. Assume X has the following probability mass function. x p(x) A. Find the mean number of drums ordered.(6 points) EX = 1(.4) + 2(.2) + 3(.2) + 4(.1) + 5(.1) = 2.3 B. Find the standard deviation of the number of drums ordered.(6 points) EX 2 = 1 2 (.4) (.2) (.2) (.1) (.1) = 7.1 σ 2 = = 1.81 σ = C. Find the mean number of gallons ordered.(4 points) 2.3x10=23 gal D. Consider a sample of five customers where the number of drums they order is independent. What is the probability that at least three of the five customers order at most three drums?(8 points) P(customer orders at most 3)=.8 Let X=# of customers that order at most 3. Binomial distribution with n=5 P(X 3) = 1 P(X 2) = =.9421

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