Chakhtoun Omar , Borough of Manhattan Community College. HW4: Midterm Review, Statistics 209 , Fall 2020 XXXXXXXXXX Name Date: Exercise 1. (10pts) Age at Inauguration. The following data represent the...

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Chakhtoun Omar , Borough of Manhattan Community College. HW4: Midterm Review, Statistics 209 , Fall 2020 [email protected] Name Date: Exercise 1. (10pts) Age at Inauguration. The following data represent the age of U.S. presidents on their respective inauguration days (through Barack Obama). 42 47 50 52 54 55 57 61 64 43 48 51 52 54 56 57 61 65 46 49 51 54 55 56 57 61 68 46 49 51 54 55 56 58 62 69 47 50 51 54 55 57 60 64 (1a) (1pt)mode (1b) (1pt) Range . (1c) (1pts)Midrange. (1d) (3pts) Give the five number Summary 1 (1e) (2pts) Construct a Box- plot. (1f) (1pt)Comment on the shape of the distribution (1g) (1pt) Do the data contain any outliers? justify your answer. Lower fence = Q1 − 1.5(Q3 −Q1) = Upper fence = Q3 + 1.5(Q3 −Q1) = 2 Exercise 2. (10pts) A Fish Story. Ethan went on a 10-day fishing trip. The number of smallmouth bass caught and released each day was as follows: 9 24 8 9 5 8 9 10 8 10 (2a) (3pts) Fill out the table below in order to compute the mean , the variance and the standard deviation of the above data. values (X) Frequency(f) f ×X f ×X2 5 8 9 10 24 Total n = ∑ f ∑ f ·X = ∑ f ·X2 = (2b) (2pts) Compute the Mean and round it. X̄ = ∑ f ×X n = (2c) (3pts) The variance and round it. s2 = n( ∑ f ×X2)− ( ∑ f ×X)2 n(n− 1) = (2d) (2pts) The standard deviation and round it s = √ s2 = . 3 Exercise 3. (5pts) Exam Scores The average score on an English final examination was 85, with a standard deviation of 5; the average score on a history final exam was 110, with a standard deviation of 8. Which class was more variable? Explain. Exercise 4. (5pts) Chebyshev’s Inequality According to the U.S. Census Bureau, the mean of the commute time to work for a resident of Boston, Massachusetts, is 27.3 minutes. Assume that the standard deviation of the commute time is 8.1 minutes to answer the following: (4a) (2.5pts) What minimum percentage of commuters in Boston has a commute time within 2 standard deviations of the mean? (4b) (2.5pts) What minimum percentage of commuters in Boston has a commute time within 1.5 standard deviations of the mean? 4 Exercise 5. (5pts) z Score for Philip Seymour Hoffman’s Age Philip Seymour Hoffman was 38 years of age when he won a Best Actor Oscar for his role in Capote. The Oscar-winning Best Actors have a mean age of 43.8 years and a standard deviation of 8.9 years. The z score formula is z = X − µ σ (5a) (1pts) What is the difference between Hoffman’s age and the mean age? (5b) (1pts) How many standard deviations is that (the difference found in part (a))? (5c) (1pts) Convert Hoffman’s age to a z score.? (5d) (2pts) If we consider usual’s ages to be those that convert to z scores between -2 and 2, is Hoffman’s age usual or unusual? 5 Exercise 6. Identification Tags (6a) (5pts) How many different 3-digit identification tags can be made if the digits can be used more than once? (6b) (5pts) If the first digit must be a 5 and repetitions are not permitted? 6 Exercise 7. (10pts) Doctor Specialties. Doctor Specialties Below are listed the numbers of doctors in various specialties by gender. (7a) (1pt) Fill out the table below. Pathology Pediatrics Psychiatry Total Male 12,575 33,020 27,803 Female 5,604 33,351 12,292 Total Suppose a passenger is selected at random. (7a) (2pt) Find P ( male ∣∣∣pediatrician) = (7b) (2pt) Find P ( pathologist ∣∣∣female) = (7c) (1pts) Are the characteristics female and pathologist independent? Ex- plain. (7d) (2pts) What is the probability that the doctor is female or psychiatric ? (7e) (2pts) What is the probability that the doctor is not a pathologist? 7 Exercise 8. (10pts) Cable Television In 2006, 86% of U.S. households had cable TV. Choose 3 households at random. Find the probability that (8a) (3pts) None of the 3 households had cable TV(2pts) (8b) (3pts) All 3 households had cable TV. (8c) (4pts) At least 1 of the 3 households had cable TV Exercise 9. (10pts) Selecting a Jury The grade appeal process at a university requires that a jury be structured by selecting five individuals ran- domly from a pool of eight students and ten faculty. (8a) (3pts) What is the probability of selecting a jury of all students? (8b) (3pts) What is the probability of selecting a jury of all faculty? (8c) (4pts) What is the probability of selecting a jury of two students and three faculty? 8 Exercise 10. Serum HDL. Dr. Paul Oswiecmiski randomly selects 40 of his 20- to 29-year-old patients and obtains the following data regarding their serum HDL cholesterol: 70 56 48 48 53 52 66 48 36 49 28 35 58 62 45 60 38 73 45 51 56 51 46 39 56 32 44 60 51 44 63 50 46 69 53 70 33 54 55 52 (10a) (5pts) Fill out the table below classes Frequency(f) class midpoint cumulative frequency class boundaries 25− 29 30− 34 35− 39 40− 44 45− 49 50− 54 55− 59 60− 64 65− 69 70− 74 (10b) (5pts) Construct a frequency histogram graph for the data 9 Exercise 11. Selecting a Card. A person selects a card from an ordinary deck of cards. If it is a black card, she wins $2. If it is a red card between or including 3 and 7, she wins $10. If it is a red face card, she wins $25; and if it is a black jack, she wins an extra $100. (11a) (2pts) Fill out the probability distribution table for this game. Selected card Winning(X) P(X) X × P(X) black card Red card between or including 3 and 7 Red face card Black jack card Total (11b) (4pts) Compute the net expected value of this game (11c) (4pts) Would the game be fair if you bet $10 dollars? Explain. 10 Exercise 12. CD Purchases. During a recent CD sale at MattÕs Music Store, the number of CDs customers purchased was distributed as follows: (11a) (1pts) Find the value of a and fill out the probability distribution table. X P(X) X × P(X) X2 × P(X) 0 0.10 1 0.23 2 0.31 3 a 4 0.09 Total (12b) (3pts)Compute the Expected value µ = ∑ X × P(X) = . (12c) (3pts)Compute the variance σ2 = ∑ X2 × P(X)− µ2 = (12d) (3pts)Compute the standard deviation σ = √ σ2 11