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 Bottles of popular cola drinks are supposed to contain 300ml of cola. There is some variation from bottle to bottle because the filling mackinery is not perfectly precise. the distribution fo the contents is normal with SD=3ml. The result of the average is 299.03. Is this convincing evidence that the mean contents of cola bottles is less than the advertised 300ml?(Find the z) A coin is tossed 10 times. What is the chance of observing 6 heads? Find the area under the x^2 curve with 10 degrees of freedom from the right of 4.86. A die is rolled 1296 times and lands on heads 650 times. Find the Z-value if it was expected to land on heads 600 times. A sample of 1,000 from a university says that 59% of students live on campus while 41% live off campus. Range from _____ to _____ is a 95% confidence interval for the students who live off campus. Scientist found orange juice helps reduce heart disease. People don't drink orange juice have 80% chance of heart disease. People who drink orange juice have 65% in a sample of 100 and SD = 4.1 Null hypothesis says orange juice doesn't help. The ave test score of students is 60. A sample of five students has ave test score of 75 with help of tutors. SD = 3.2 Null hypothesis : tutor doesn't help, ave score is still 60 In a sample of 40, ave age in 12th grade of school A = 17 SD = 0.2 In a sample of 20, ave age in 12 th grade of school B = 19 SD = 0.5 What is the SE for difference? What is the SE for a box with 60 red marbles, and 90 blue ones The average weight of the girls in the high school is 130lbs, and the SD is 30. Their average height is 70 inches, and the SD is 3. r=0.48 For a person who weight 148lbs will probably have height of __? The following distribution is given: Ave x=185 SDx=80 Ave y=120 SDy=45 r=-.75 Suppose y=170. What is the regression estimate for predicting the value of x from that of y? There has been a study which relates the scores of math and biology classes. The results of average test scores and SD's for each class are as follows: Ave Math score - 65 Ave Biology score - 70 SD - 5 SD - 10 r - .6 If a student has an average score of 70 in math, predict his biology score. In our Math 108 class the midterm scores average was about 55 with an SD of 20, as do scores on the final. The correlation between midterm scores and final scores is about 0.75. Estimate the average final score for the students whose midterm scores were 75. A study was done in Rye High School for the heights and weights of girls at the age of 16. The average weight was 110lbs with an SD of 10lbs and the average height was 64 inches with an SD of 2 inches. The correlation coeficient is 0.80. Predict the weight for a 16 year old girl whose height is 70 inches. The correlation between mid term and final is 0.8. The scatter diagram is football-shaped. Predict the percentile rank on the final for people rank 95% on mid term. A survey was conducted to estimate the correlation between teen Weed- Smokers and teen Tabacco- Smokers. The Weed- Smoker, puffed, on average 10 Weed- cigarettes per week with an SD of 2.Tabacco - Smokers smokes an average of 60 cigarettes per week with an SD of 5. Estimate the average Tabacco - Cigarettes smoked per week for a teen who smokes 12 Weed- Cigarettes. The correlation coefficient is 0.7. In a football- shaped diagram, for values X under 140 what is the percent of Y over 120? Use the following information. AveY=100,SDY=9. AveX=150,SDX=20. r=0.7. If r=0.5 for expected salary and educational level, what is the expected salary for people at the average educational level. salary avg=30,000, SD=10,000. educational level=12 yrs, SD=4 yrs. Find the error for this data: avgX=90, SD=7, avgY=70, SD=5, r=0.6. Wal-Mart sold 12,000 X-mas Trees in '97 w/ an SD of 300 in each of its stores. The sale of lights totaled to be 11,000 has the same SD. r=0.9, How many lights does it sell if one particular store sold 15,000 X-Mas trees. A school is working on the relationship between SAT and the first year greade. Ave SAT score=1160, SD=18. Ave first yera=83, SD=6, r=0.6 Find the R.M.S. Error. The results midway through a new weight loss program for women showed an average weight loss of 45 lbs, with an SD of 20. The final results showed an average weight loss of 50 lbs, with an SD of 10. The correlation between midpoint and final results was .6 For each member of this program, the final weight loss was predicted from the midpoint weight loss using the regression line. Compute the r.m.s. error for regression. A study was done to see if a person's parent's income had any effect on his or her own income. These were the results: Ave Parents income - 67,000 Ave Child's income - 58,000 SD - 15,000 SD - 10,000 r - .8 Compute the R.M.S. Error from the parent's income. The Albany Research Committee conducted a study on students that attend the Albany School District. The average height of students age 7 was about 3ft. 7 inches; the SD is 1.4. The average height of students age 17 is about 5ft. 8 inches; the SD is 2.3 inches. The r=0.68. Find the r.m.s. error for the regression of the height at 17 from the height at 7. The average weight of women at age 18 is 120 with an sd of 4. The average weight for women at age 21 is 137 with an sd of 6. With the r being equal to .4, compute the rms error for regression of weights at age 18 from weights at age 21. There were scores taken on the students of Suny Albany in the Business Law midterm and final. The average score on the midterm was 70 with an SD of 20. The average score on the final was 75 with an SD of 15, and the correlation coeficient was 0.60. Find the r.m.s. error for the regression line predicting midterm from final. ave weight = 130 lb SD = 10 lb ave height = 5'5" SD = 1.5" Compute the RMS error for regression of height from weight when r = 0.5. A shoe store is finding the relationship between teh heights and the shoe sizes. It is summarized as followers. Ave Height=75 inches, SD=5 Ave shoe size=8, SD=1.5, and r=0.45 Find the regression equation for predicting shoe size from the height. The following distribution is given: Ave x=185 SDx=80 Ave y=120 SDy=45 r=-.75 What is the slope of the regression line? The New York Knicks trainer has found a new jump training program to help players improve their vertical. The predicted improvement is 1inch per 25 hours of training, but the first 40 hours will have no results because it takes time for the body to adjust to the program. How many hours does a rookie need to spend on the program to improve his vertical 6 inches? The equation of regression line is y = 0.5x + 2. r = 0.7 ave of x value = 2, find equation of SD line. Suppose that both parents in a family carry genes for blood types A and B. The blood types of their children are independent and each child has probability 1/4 of having blood type A. there are 4 children in the family. Find the probability of two children having blood type A. You have a biased coin that lands heads 65% of the time and lands tails 35% of the time. You flip it 6 times. What is the probability you get exactly 5 heads? If a die is rolled 20 times, find the chance of getting exactly 4 aces. A roulette wheel has 38 numbers, including 0 and 00. What is the probability of 0 or 00 coming up in once 10 consecutive spins of the wheel? If a coin is tossed 5 times, what is the chance of observing 3 heads? A deck of shuffled card, draw 10 times with replacement. What is the probability of getting exactly one "King"? A coin is tossed 5 times, what is the chance of exactly two heads? A coin is tossed 10 times, what is the chance of 5 heads A factory is duirng a survey. A simple random sample of 2500 workers have 1400 female workers. Find the standard error for the percentage. 200 draws are made from a bag of 5 tickets. Each ticket was labelled individually with a number, as follows: 2 2 6 8 9 Compute the expected sum and standard error for sum. In a city of 50,000 a random sample of 1,000 was taken to measure yearly incomes. Of the sample, 500 earned 20,000 or less, 350 earned between 20,000 and 70,000 while 150 earned over 70,000. Find the SE for the percentage of residents who earn more than 70,000 dollars. There is a town of 50,000 people which has 30,000 of the population that are female. A survey of 500 people at randon from this town is taken. Find the S.E. for the percent of female in the sample. 4.2% 1.3% 1.2% 2.2% 3.3%

Carlos Rodriguez <carlos@math.albany.edu>
This problem was contributed by a student in Elementary Statistics. It is offered as it is with no warranty of any kind
Last modified: Wed May 13 12:29:11 EDT 1998