mth 2200

Anonymous
timer Asked: Nov 26th, 2017

Question Description

10 questions

1. Monthly salaries of 22 executives are as follows: 3319 2304 3186 3093 3259 3457 2952 3272 3328 3365 3232 3234 3302 3105 3203 3017 3046 3130 3408 3270 2913 3192 a) Make a stemplot of this data by rounding to the nearest 10 so that stems are hundreds and leaves are tens. b) What are main features of the stemplot? 2. Here is a list of 12 Smurf heights, in inches: 17, 6, 14, 11, 23, 13, 9, 7, 8, 11, 8, 12 a) Find the mean and standard deviation for the data set. b) Find Five-Number Summary: c) Use the 1.5 IQR rule to detect any outlier present in this data set. d) Draw a box plot or modified box plot for this data on the given ruler. 3. The Final Exam scores of Business Calculus in Fall 2011 are approximately normally distributed with a mean of 80 and a standard deviation of 12 pts. A student who took the final exam is randomly selected, a) What is the probability of the student scored higher than 90 on the final? b) What is the probability of the student scored between 78 and 90 on the final? c) If 25 students are randomly selected from this population, what is the probability that the mean score is higher than 90 on the final? d) Find a cut off score x so that only 15% of all students got less than x. 4. The data below are the final exam scores of 8 randomly selected history students and the number of hours they slept the night before the exam. ( x  5, s x =2.27, y  75.25 , s y =10.16) Hours, x Scores, y xi  x sx yi  y sy 3 65 -0.88 6 80 0.44 3 60 ( ) 8 88 1.32 2 66 -1.32 5 78 0 -1.01 0.47 -1.50 1.25 -0.91 ( ) 5 85 0 8 80 1.32 0.96 0.47 a) What are the explanatory and response variables? Are they categorical or quantitative? b) Make a scatterplot. Label the axes. Interpret the scatterplot (Form, direction, strength). c) Fill in the blanks, then calculate r = correlation coefficient between hours of sleeping and history exam score. Verify your answer with part (b). d) Find the least square regression line. Does the line show a success in predicting history exam score with hours of sleeping? 5. Consider a random variable Y, the density curve ( P( y ) ) of the outcome has a constant height between 0 and 4, and height 0 elsewhere as shown below: P( y ) 0 2 4 y a) Is the random variable Y discrete or continuous? Circle one. b) What is the probability that Y is less than 2? c) What is the probability that Y is greater than 3? 6. The Denver Post stated that 80% of all new products introduced in grocery stores are taken off the market within 2 years. If a grocery chain introduces 100 new products, a) what is the mean and standard deviation of the taken-off new product count within 2 years? b) what is the probability that within 2 years 58 fail? c) what is the approximate probability that within 2 years 58 or less fail? 7. By examining the past driving records of 640 randomly selected drivers over a period of 1 year, the following data were obtained. Under 25 ( U ) Over 25 ( U ) Accident (A) No Accident ( A ) 40 85 5 510 a) What is the probability of a driver having an accident? b) What is the probability of a driver having an accident, given that the person is under 25? c) What is the probability that a driver is over 25, given that the driver has no accident? d) Are events A and U independent? Explain. 8. The distribution of blood cholesterol level in the population of young men aged 20-34 years is close to Normal with standard deviation   41 mg/dL. You measure the blood cholesterol of 14 cross –country runners. The mean level is x  172 mg/dL. a) Find a 95% confidence interval for the mean level  among all cross-country runners . b) How large a sample is needed to cut the margin of error to  5 mg/dL? 9. In a random sample of 16 DVD players brought in for repairs, the average repair cost was $ 50 and the standard deviation was $ 10. Assume that the repair cost of computers follow a normal distribution. Construct a 95% confidence interval for the mean repair cost of DVD players. 10. Consider the following table that lists SAT scores before and after a sample of five students took a preparatory course. Student SAT score before course SAT score after course 1 700 720 2 830 830 3 840 830 4 860 880 5 690 700 Assume that SAT scores are normally distributed. Is there any evidence that the preparatory course help to improve the SAT scores?

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