SMAM 345 Exam 1 Name. 1. The following data represent the number of miles per gallon achieved on the highway for small cars for the model year 2008.

Transcription

1 SMAM 34 Exam 1 Name 1. The following data represent the number of miles per gallon achieved on the highway for small cars for the model year A. Complete the stem and leaf display(4 points) B. Make a five number summary.(4 points) C. Find the inter quartile range and determine whether there are any outliers. (4 points) IQR=4 1.IQR=6 23 is borderline.

2 D.Draw a boxplot.(4 points) E.Comment on the shape of the data.(4 points) Data is skewed to the left. 2. The fitted line plot below is for data is the weight vs. mpg. for 11 cars of different brands. The data follows. Car Weight(lb) Miles per gallon(mpg) Buick Lucerne Cadillac De Ville Chevrolet Malibu Chrysler Sebring Sedan Dodge Neon Dodge Charger Ford Focus Linco ln LS Mercury Sable Pontiac G Saturn Ion

3 A. How many mpg would you predict for a 200 lb car? Give your answer to the nearest integer.(3 points) Mpg= (200)=27.29 B. What is the correlation coefficient?(3 points) r =.929 =.9638 C. Based on the correlation coefficient, how well the line appears to fit the data in the graph and the percentage of the variation accounted for by the regression line comment on the adequacy of the model. [A good model usually accounts for at least 80% of the variation has a correlation with absolute value 0.9 or higher and has a scatter plot that approximates a straight line](4 points) The model is quite adequate. The points on the scatterplot are close to a straight line. The model accounts for 92.9%>80% of the variation. The correlation coefficient is.9638 and has absolute value greater than A car approaching an intersection can go right(r) left (L)or straight(t). A. Suppose two cars are observed. What are the elements of the sample space? ( points) {LL,LR,LS, RL,SL,SR,RS,RR,SS}

4 B. Assume that the probabilities that a car would go right, left, or straight are equal. Assume that the two cars act independently. What is the probability at least one car goes straight?( points) A={SR,RS,SL,LS,SS} Each element has probability 1/9 because for a single car the probability of R,L or S =1/3. Thus, P(A)=/9 4. Consider randomly selecting a student at a university.the probability that he/she has a Visa credit card is 0.. The probability he has a Mastercard is 0.4. The probability that he has at least one of these cards is 0.6. A. What is the probability he has both cards?( points) P(M P) = P(M) + P(V) P(M V) = =.2 B. What is the probability he has neither card?( points) P(M ' V') = P(M V)' = 1 P(M V) = 1.6 =.3 C. Suppose the student has at least one of the cards. What is the conditional probability he/she has both cards?( points) P(M V M V) = P(M V) P(M V) =.2.6 = Shortly after being put into service, some busses manufactured by a certain company have developed cracks on the underside of the main frame. In a particular city there are 2 busses with eight with cracks. A. How many ways can a sample of busses from the 2 be selected?( points)

5 2 = 3130 B. What is the probability that at least one of the busses in the sample in A has a crack?( points) =.883 C. What is the probability that 2 or 3 busses in the sample in A is has a crack? ( points) = A company that manufactures video cameras produces a basic model and a deluxe model. During the past year 40% of the cameras sold have been the basic model. Thirty percent of the customers that purchase a basic model buy an extended warranty while 0% of the customers that purchase a deluxe model do so. A. What is the probability that a customer purchases an extended warranty? (7 points) W=extended warranty B=basic D=deluxe P(W B) =.30,P(W D) =.0,P(B) =.40,P(D) =.60 P(W) = P(W B)P(B) + P(W D)P(D) = (.30)(.40) + (.0)(.60) =.42

6 B. Assuming that a customer purchases an extended warranty what is the probability that he/she bought the basic model?(7 points) P(B W) = P(W B)P(B) P(W) = (.30)(.40).42 =.287 C. C. Assuming that a customer did not purchase an extended warranty what is the probability that he/she bought the basic model?(6 points) P(W' B) = = 1 P(W' B) P(B) P(W B) P(B) = P(B) P(W B) P(B) = 1 P(W B) = 1.30 =.70 P(B W') = P(W' B)P(B) P(W') = (1 P(W B))P(B) 1 P(W) = (.70)(.40).8 = A system has two subsystems in series. Each subsystem has two components in parallel. Each component has the same reliability and all of the components work or fail independently of one another. The system reliability is What is the reliability of each component? (10 points) (1 (1 R) 2 ) 2 = (1 R) 2 =.99 (1 R) 2 =.01 1 R =.1 R =.9