# Questions on Algebra: Probability and statistics answered by real tutors!

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 Algebra: Probability and statistics Solvers Lessons Answers archive Quiz In Depth

 Question 436445: . If an average of 60 customers are served per hour, then one customer arrives every A. 1 minute B. 60 minutes C. 12 minutes D. 10 minutes Click here to see answer by rfer(12660)

 Question 436448: The size of the sampling error is A. Directly related to the sample size, i.e., the larger the sample size, the larger the sampling error. B. Directly related to the population mean, i.e., the larger the mean, the larger the sampling error. C. Inversely related to the sample size, i.e., the larger the sample size, the smaller the sampling error. D. Inversely related to the population standard deviation, i.e., the smaller the standard deviation, the larger the sampling error. Click here to see answer by robertb(4012)

 Question 436481: A class has 11 students who are to be assigned by lot. What is the probability that the students will be arranged in order from shortest to tallest? ( Assume that no two students are the same height.) Click here to see answer by robertb(4012)

 Question 436450: Recently, a university surveyed recent graduates of the English Department for their starting salaries. Four hundred graduates returned the survey. The average salary was \$25,000. The population standard deviation is \$2,500. A 95% confidence interval is constructed. What does the confidence interval mean? A. The population mean is in the interval B. The population mean is not in the interval C. The likelihood that any confidence interval based on a sample of 400 graduates will contain the population mean is 0.95 D. There is a 5% chance that the computed interval does not contain the population mean Click here to see answer by robertb(4012)

 Question 436447: . A study of a company's practice regarding the payment of invoices revealed that an invoice was paid an average of 20 days after it was received. The standard deviation equaled five days. Assuming that the distribution is normal, what percent of the invoices were paid within 15 days of receipt? A. 15.87% B. 37.91% C. 34.13% D. 86.74% Click here to see answer by robertb(4012)

 Question 436446: Sixty percent of the customers of a fast food chain order a hamburger, french fries and a drink. If a random sample of 15 cash register receipts is selected, what is the probability that 10 or more will show that the above three food items were ordered? A. 1.000 B. 0.186 C. 0.403 D. 0.000 Click here to see answer by robertb(4012)

 Question 436404: Please show me how to do this problem. I got answers but they were not correct. [ a ][ ][ ][ ][ ][ ][ ] [ ][ ][ b ][ ][ ][ ][ ] [ ][ ][ ][ c ][ ][ ][ z ] If a route (with no backtracking) from A to Z is randomly chosen, what is the probability that the route passes through point B? Answer in fraction. Given that a route passes through B, what is the probability that it also passes through point C? Answer in fraction. Click here to see answer by robertb(4012)

 Question 436505: a traffic light is red for 25 sec, yellow for 5 sec, and green for 55 sec. What is the probability that when you reach the light it is not green. Click here to see answer by shree840(260)

 Question 436527: I have Dyscalclia (Math Dyslexia) and I am in tears trying to figure these out. Please help me get some extra credit points. A company has determined that the mean number of days it takes to collect on its accounts receivable is 36 with a standard deviation of 11 days. What is the probability that a single AR account takes more than 30 days to collect? The Dilmart Company has 8,000 parts in inventory. The mean dollar value of these parts is \$10.79 with a standard deviation equal to \$3.34. Suppose the inventory manager selected a random sample of n = 64 parts from the inventory and found a sample mean equal to \$11.27. What is the probability of getting a sample mean at least as large as \$11.27? A vaccine is 90 percent effective. What is the probability that it is effective for two or more individuals out of 20 individuals? Use the normal approximation to the binomial distribution. The quality control manager of a tire company wishes to estimate the tensile strength of a standard size of rubber used to make a class of radial tires. The historical population standard deviation is 35 pounds. A random sample of 61 pieces of rubber from different production batches is subjected to a stress test. The test measures the force needed to break the rubber in pounds. According to the sample results, the average pressure is 238.4 pounds. Determine the 98% confidence interval. The average weight of an airline passenger’s suitcase is 45 pounds. The standard deviation is 2 pounds. If 17% of the suitcases are overweight, find the maximum weight allowed by the airline. Assume the variable is normally distributed. See curve drawn on the board. Recently, a report in a financial journal indicated that the 90 percent confidence interval estimate for the proportion of investors who own one or mutual funds is 0.9 with a margin of error of ± 0.02 points. Given this information, calculate the required sample size. Click here to see answer by stanbon(57347)

 Question 436502: Blue Chips and Red Chips A bag contains 3 blue chips and 2 red chips. Chi and Dolly play the following game. Chi selects one chip at random from the bag. If Chi selects a blue chip, Dolly gives Chi \$5. If Chi selects a red chip, Chi gives Dolly \$8. * a) Determine Chi’s expectation. * b) Determine Dolly’s expectation. You can put this solution on YOUR website! Blue Chips and Red Chips A bag contains 3 blue chips and 2 red chips. Chi and Dolly play the following game. Chi selects one chip at random from the bag. If Chi selects a blue chip, Dolly gives Chi \$5. If Chi selects a red chip, Chi gives Dolly \$8. -------------------- Random gain values for Chi: 5, -8 Corresponding Probabilities: 3/5, 2/5 ------ * a) Determine Chi’s expectation. E(x) = 5(3/5)-(8)(2/5) = 3-16/5 = -1/5 = -20 cents -------------------------------------------------------- * b) Determine Dolly’s expectation. Ans: +20 cents Click here to see answer by stanbon(57347)

 Question 436573: a bag contains 30 marbles with 18 blue ones and 12 red ones. If you reach into the bag and draw out marbles one at a time until you have three in your hand, what is the probability that they are all blue? Click here to see answer by stanbon(57347)

 Question 436490: 2. Assume the body temperatures of healthy adults are normally distributed with a mean of 98.20 °F and a standard deviation of 0.62 °F (based on data from the University of Maryland researchers). a. If you have a body temperature of 99.00 °F, what is your percentile score? b. Convert 99.00 °F to a standard score (or a z-score). c. Is a body temperature of 99.00 °F unusual? Why or why not? d. Fifty adults are randomly selected. What is the likelihood that the mean of their body temperatures is 97.98 °F or lower? e. A person’s body temperature is found to be 101.00 °F. Is the result unusual? Why or why not? What should you conclude? f. What body temperature is the 95th percentile? g. What body temperature is the 5th percentile? h. Bellevue Hospital in New York City uses 100.6 °F as the lowest temperature considered to indicate a fever. What percentage of normal and healthy adults would be considered to have a fever? Does this percentage suggest that a cutoff of 100.6 °F is appropriate? Click here to see answer by stanbon(57347)

 Question 436521: if a five digit number is chosen at random, what is the probability that the product of the digits is 20? Click here to see answer by Edwin McCravy(8909)

 Question 436623: There are red, blue and green marbles in a bag. The probability of randomly choosing a blue marble is .3 and the probability of randomly choosing a blue or red marble is .7. If there is a total of 20 marbles how many marble of each color are in the bag? Click here to see answer by stanbon(57347)

 Question 436616: About 90% of the general population is right-handed. A researcher speculates that artists are less likely to be right-handed than the general population. In a random sample of 100 artists, 83 are right-handed. Which of the following best describes the p-value for this situation? Click here to see answer by stanbon(57347)

 Question 436658: A shopper wanted to test whether there was a difference in the average waiting times at the check-out counter among 5 different supermarkets. She selected a random sample of 20 shoppers from each of the five supermarkets. What is the null hypothesis for this situation? A) The average waiting time to check out is 25 minutes for all five supermarkets. B) The average waiting time to check out is the same for all five supermarkets. C) The average waiting time for each of the 100 shoppers is different. D) The average waiting time to check out is not the same for all five supermarkets Click here to see answer by stanbon(57347)

 Question 436636: The probability that federal income tax returns will have 0,1,or 2 errors is 0.73, 0.23, and 0.04, respectively. If 10 randomly selected returns are audited, what is the probability that eight will have no errors, two will have one error, and none will have two errors? Click here to see answer by stanbon(57347)

 Question 436768: find n for a 96% confidence interval for p with e=0.024 using an estimate of p=0.8 ( round to the nearest whole number) Click here to see answer by stanbon(57347)

 Question 436784: in an election for school president, the loser recieved 30% of the winner's votes. If 702 votes were cast, how many did each recieve? Click here to see answer by rfer(12660)

 Question 436749: 1- How many different ways could you select 5 stocks from a total of 10 candidates? 2-Using the rule of multiplication, prove that the probability of drawing a King of Spades is 0.0192. Click here to see answer by jorel1380(2518)

 Question 436794: A rectangle is to be inscribed under the arch of the curve y=4cos(x/2) from x = - (pi)radians and x= (pi) radians. What are the dimensions of the rectangle with the largest area? My professor wants me to work in radians and use Newton's method to find the zero of the first derivative. Any help would be greatly appreciated. I know the area and derivative is the following.. A= (2x)(4 cos (x/2)) = 8xcos (x/2) dA/dx = 8 cos (x/2) - 4xsin(x/2) I don't know what to do next when the equation is equal to zero. Click here to see answer by richard1234(5390)

 Question 436745: a binomial distribution has a mean equal to 12 and a standard deviation equal to 2.683. Find n and p. Click here to see answer by robertb(4012)

 Question 436815: Suppose you were the manufacturer of a new and improved light bulb that you claim has an average service life more than twice the life of your nearest competitor’s product. You want to test your product to be sure. You test 500 of your bulbs in the lab and find that the average life of your bulbs is 2021 hours. Your competitor claims an average service life of 1000 hours. What hypotheses would you test? State the null and alternative hypotheses both verbally and algebraically. Note: Please do not try to actually complete this hypothesis test. You can't do it, because I don't have the necessary data. Even if I had the necessary data, the scenario was carefully chosen for which I do not know the mathematical equation for the test statistic. For that matter, I'm not sure I know it -- there may not be one. This specific scenario serves as an exercise in correctly forming hypotheses. If you can correctly form these hypotheses, you can probably set up any hypothesis test correctly. Click here to see answer by robertb(4012)

 Question 436818: Hi! I was hoping I could get some help with this problem. Thanks! It costs more to produce defective items–-since they must be scrapped or reworked–-than it does to produce non-defective items. This simple fact suggest that manufacturers should ensure the quality of their products by perfecting their production processes rather than through inspection of finished products. In order to better understand a particular metal stamping process, a manufacturer wishes to estimate the mean length of items produced by the process during the past 24 hours. A. How many parts should be sampled in order to estimate the population mean to within 0.3 mm with 95% confidence. Previous studies of this machine have indicated that the standard deviation of lengths produced by the stamping operation is about 2 mm. B. Time permits the use of a sample size no larger than 100. If a 95% confidence interval for ì is constructed using n = 100, will it be wider or narrower than would have been obtained using the sample size from part a? Click here to see answer by stanbon(57347)

 Question 436793: Sorry...this is more of a calculus question but I really need some help. The following experimental data set has been collected {(xi, yi)} = { (0.6, 10), (1.3, 20), (2.1, 30), (3.6, 50), (7.3, 100) }. Find the best straight line y = mx that fists the data by using a method that minimizes the error squared: E =n=1 (y- mx)^2 = (y1 - mx1)^2 + (y2- mx2)^2 + ... + (yn - mxn)^2. The task is to find slope, m of the straight line by minimizing E using the data set given above. Please help. I don't know where to begin. Click here to see answer by Edwin McCravy(8909)

 Question 436881: Do students at various universities differ in how sociable they are? Twenty-five students were randomly selected from each of three universities in a region and were asked to report on the amount of time they spent socializing each day with other students. The result for University X was a mean of 5 hours and an estimated population variance of 2 hours; for University Y, ; and for University Z, . What should you conclude? Use the .05 level. (a) Use the steps of hypothesis testing, (b) figure the effect size for the study; and (c) explain your answers to parts (a) and (b) to someone who has never had a course in statistics. Click here to see answer by stanbon(57347)

 Question 436879: The game of heads up is played by flipping two coins. If they both land heasds up, you win \$12. If only one lands heads up,you win\$12. If no conis land heads up, you win \$8. If you pay \$15 to play the game each time the coins are flipped, is the game a fair game? Click here to see answer by stanbon(57347)

 Question 436876: If a family has 5 children, what is the probability that all 5 are girls. Click here to see answer by Alan3354(30993)

 Question 436931: The odds in favor of horse winning a race are posted as 8:7. find the probability that the horse wlll lose the race. Click here to see answer by ewatrrr(10682)

 Question 436898: (This problem has 4 different questions.) Twenty-five percent of the employees of a large company are minorities. A random sample of 7 employees is selected. A) what is the probability that the sample contains 4 minorities? B) what is the probability that the sample contains fewer than 2 minorities? C) what is the probability that the sample contains exactly 1 non-minority? D) what is the expected value of minorities in the sample? Click here to see answer by ewatrrr(10682)

 Question 437140: The level of significance is always A. the maximum allowable probability of type II error B. the maximum allowable probability of type I error C. the same as the confidence D. the same as the p-value E. 1 - P(type II error) Click here to see answer by stanbon(57347)

 Question 437142: A 90% confidence interval for a population mean is determined to be 800 to 900. If the confidence is increased to 95% confidence while the sample statistics and sample size remain the same, the confidence interval for mui A. becomes narrower B. becomes .05 C. does not change D. becomes wider E. becomes .025 Click here to see answer by stanbon(57347)

 Question 437225: f(x)= 3x+1/k for x= (1,3,5,7,9,11) 0 otherwise a. Find the value of k that will make this function a “true” pdf. b. Find the mean, variance and standard deviation for this random variable. c. Find P(x>3) d. Find P(1≤x≤9) e. Find P(x<9) Click here to see answer by robertb(4012)

 Question 437222: An IQ test is approximately normally distributed witha mean of 100 and standard deviation of 15. What is the probability that a randomly chosen individual has an IQ score of 110 or higher? Click here to see answer by stanbon(57347)

 Question 437220: 2 Infant mortality rates (IMR) (i.e. the probability of a child dying before the age of one year) vary by race. In 2001 in the USA the IMR for Caucasians was 0.0057 and for African Americans it was 0.0133. Suppose three Caucasian children are selected at random. a. What is the probability all three will live past the age of one year? b. What is the probability that at least one will die within one year? c. Repeat part a and b for three randomly selected African American children Click here to see answer by stanbon(57347)

 Question 437211: Scores on the Stanford-Binet Intelligence scale have a mean of 100 and a standard deviation of 16, and are presumed to be normally distributed. A person who scores 68 on this scale has what percentile rank within the population? Show all work as to how this is obtained. Click here to see answer by stanbon(57347)

 Question 437210: Household income does not tend to follow a normal distribution in a particular state, yet average income is approximately \$45,000/year in this state, with a standard deviation of about \$9000. Within what income range would approximately 75% of the household incomes lie within this state? having trouble forming the right way to put the information in an equation. Click here to see answer by stanbon(57347)

 Question 437179: there are 8 green. 10 rf and 12 yellow balls in a basket if we pick a ball at random that is the probabitity that the ball is not gree and red Click here to see answer by stanbon(57347)

 Question 437158: The average price for a new car is \$16,000 and the standard deviation is \$1,500. What is the z score for a car price (x) = \$19,000 Click here to see answer by stanbon(57347)

 Question 437144: You have sampled 25 students to find the mean SAT scores at Morris Knolls High School. A 95% confidence interval for the mean SAT score is 900 to 1100. Which of the following statement gives a valid interpretation of this interval? A. 95% of the 25 students have a mean score between 900 and 1100. B. 95% of the population of all students at Morris Knolls have a score between 900 and 1,100. C. If this procedure were repeated many times, 95% of the resulting confidence intervals would contain the true mean SAT score at Morris Knolls. D. If this procedure were repeated many times, 95% of the sample means would be between 900 and 1100. E. If 100 samples were taken and a 95% confidence interval was computed, 5 of them would be in the interval from 900 to 1100. Click here to see answer by stanbon(57347)

 Question 437155: A spinner is divided in half with one half A and the other B. what is the probability that a spinner spun eight times will land on B at least four times? Click here to see answer by stanbon(57347)

 Question 437125: the final exam in a math coures consists of 40 multiple-choise question. each question has 4 possible answers, and only 1 of them is correct. an unprepared student makes random guesses for all of the answers. find the mean and standard deviation for the number of correct anwers for such student. Click here to see answer by stanbon(57347)

 Question 437035: twenty percent of the employees of a large company are female. find the probability that in a random sample of 15 employees, at least two are female. Click here to see answer by stanbon(57347)

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