Spring 2017 Math 54 Test #2 Name:
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1 Spring 2017 Math 54 Test #2 Name: You may use a TI calculator and formula sheets from the textbook. Show your work neatly and systematically for full credit. Total points: (6) Suppose P(E) = 0.37 and P(F) = 0.22 a. Find P(E or F) if E and F are mutually exclusive events. b. Find P(E and F) if E and F are independent events. 2. (12) In 2013, there were 32,719 traffic fatalities in the United States. Of these, 10,076 were alcohol related. a. What is the probability that a randomly selected traffic fatality in 2013 was alcohol related? b. What is the probability that a randomly selected traffic fatality in 2013 was not alcohol related? c. What is the probability that three randomly selected traffic fatalities in 2013 were all alcohol related? d. What is the probability that of three randomly selected traffic fatalities in 2013 at least one was alcohol related? 3. (5) The average 20- to 29-year-old man is 69.6 inches tall, with a standard deviation of 3.0 inches. What is the z- score of a 75-inche man?
2 4. (9) A standard deck of cards contains 52 cards. One card is randomly selected from the deck. a. Compute the probability of randomly selecting a two or three from a deck of cards. b. Compute the probability of randomly selecting a two or a black card from a deck of cards. c. Compute the probability of randomly selecting a face card or a heart from a deck of cards. 5. (8) A fair die is rolled twice. a. Find the probability of getting two numbers whose sum is greater than 10. b. Find the probability of getting two numbers whose sum is 5 or one of the numbers is (6) Consider the following contingency table, which relates the numbers of applicants accepted to a college and gender. Accepted Denied Male Female a. What proportion of males was accepted? What proportion of female was accepted? b. One applicant is randomly selected, find the probability of selecting a male or is accepted to a college.
3 7. (3, 6) The data below represent the age of the mother at the time of her first birth for a random sample of 30 mothers a. Find the five number summary. b. Construct a boxplot of the data and describe the shape of the distribution. 8. (9) The following data represent the miles per gallon of a random sample of SMART cars with a three-cylinder 1.0-liter engine a. Compute the z-score corresponding to the individual who obtained 36.3 miles per gallon (Note that you need to compute the mean and standard deviation first) b. Determine the quartiles and find the interquartile range, IQR. c. Determine the lower and upper fences. List outliers, if any.
4 9. (20) The following data represent the number of days absent, x, and the final grade, y, for a sample of college students in a general education course at a large state university. No. of absences, x Final grade, y a. Draw a scatter diagram of the data treating number of absences as the explanatory variable. Comment on the type of relation that appears to exist between number of absences and final grade. b. Find the linear correlation coefficient. Test whether there is a linear correlation between the number of absences and final grade (Compare r with critical value to make decision). c. Find the least-square regression line treating number of absences as the explanatory variable and final grade as the response variable. Predict the final grade for a student who misses five class periods. d. Interpret the slope and y-intercept, if appropriate.
5 e. What proportion of the variability in final grade is explained by the relation between number of absences and final grade? List at least two lurking variables. 10. (5) A highly selective boarding school will only admit students who place at least 1.75 z-scores above the mean on a standardized test that has a mean of 110 and a standard deviation of 12. What is the minimum score that an applicant must make on the test to be accepted? 11. (12) The wind chill factor depends on wind speed and air temperature. The following data represent the wind speed (in mph) and wind chill factor at an air temperature of 15 degree Fahrenheit. Wind speed, x (mph) Wind Chill factor, y Predicted value, a. Find the least-square regression line. Residual, b. Compute for each given x value (fill in values in the above column); compute the residual (fill in values in the above column). c. Plot the residuals against the wind speed. Do you think that least-square regression line is a good model? (Is there any noticeable pattern?)
Spring 2016 Math 54 Test #2 Name: Write your work neatly. You may use TI calculator and formula sheet. Total points: 103
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