1. A researcher wanted to get the percentage of college students that major in Business. The researcher got information from 5 colleges with a total of 11 thousand students and found that 1.5 thousand of them majored in Business. a. What is the population? b. What is the sample? c. What is the parameter? d. What is the symbol for this parameter? e. What is the statistics? f. What is the symbol for this statistics? 2. A researcher wants to determine the average amount of minutes it takes for a medicine to reduce headache pain for adult males. The researcher contacted 107 subjects to participate in the study, but only got results from 79 of the subjects. The average time it took for the medicine to reduce headache pain for these subjects was 27 minutes. a. What is the population? b. What is the sample? c. What is the parameter? d. What is the symbol for this parameter? e. What is the statistics? f. What is the symbol for this statistics? 3. A business has Brand A, Brand B and Brand C of the same product. Market research has shown that 43% of costumers that purchase this product will choose Brand A. An organization conducts a poll of 100 consumers. Find the probability that 40 to 45 of the 100 consumers will prefer Product A, given the 43% brand preference is correct. 4. A manufacturing machine has a 4% defect rate. If 4 items are chosen at random, what is the probability that at least one will have a defect? 5. The television show September Road has been successful for many years. That show recently had a share of 17, meaning that among the TV sets in use, 17% were tuned to September Road. Assume that an advertiser wants to verify that 17% share value by conducting its own survey. A pilot survey begins with 14 households that have TV sets in use at the time of a September Road broadcast. a) Find the probability that none of the households are tuned to September Road. P(none) = b) Find the probability that at least one household is tuned to September Road. P(at least one) = c) Find the probability that at most one household is tuned to September Road. P(at most one) = d) If at most one household is tuned to September Road, does it appear that the 17% share value is wrong? (Hint: Is the occurrence of at most one household tuned to September Road unusual?) Use a value of 5% or lower for "unusual". 6. After being rejected for employment, Kim Kelly learns that the Bellevue Credit Company has hired only three women among the last 17 new employees. She also learns that the pool of applicants is very large, with an approximately equal number of qualified men as qualified women. Help her address the charge of gender discrimination by finding the probability of getting three or fewer women when 17 people are hired, assuming that there is no discrimination based on gender. 7. A small regional carrier accepted 21 reservations for a particular flight with 20 seats. 13 reservations went to regular customers who will arrive for the flight. Each of the remaining passengers will arrive for the flight with a 56% chance, independently of each other. Give answer to 4 decimal points or copy and paste your answers from Excel. a) Find the probability that overbooking occurs. b) Find the probability that the flight has one or more empty seats. c) Find the probability that the flight has no empty seats and no overbooking. 8. The probability that you will win a game is 0.37. a) If you play the game 1150 times, what is the most likely number of wins? b) Find the standard deviation for the probability distribution. = c) The range rule of thumb specifies that the minimum usual value for a random variable is -2 and the maximum usual value is +2. You already found and from parts a and b. Use the range rule of thumb to find the usual range of values. Usual values = 9. A manufacturer knows that their items have a normally distributed length, with a mean of 16 inches, and standard deviation of 1.9 inches. a. If one item is chosen at random, what is the probability that it is less than 21 inches long? b. If one item is chosen at random, what is the probability that it is greater than 19 inches long? c. If one item is chosen at random, what is the probability that it is between 15 and 21 inches long? 10. An electronic product takes an average of 3 hours to move through an assembly line. If the standard deviation is 0.6 hours, what is the probability that an item will take between 3 and 4.8 hours to move through the assembly line? 11. The systolic blood pressure of adults in the USA is nearly normally distributed with a mean of 119 and standard deviation of 18. Someone qualifies as having Stage 2 high blood pressure if their systolic blood pressure is 160 or higher. a. Around what percentage of adults in the USA have stage 2 high blood pressure? b. If you sampled 500 people, how many would you expect to have BP> 160? c. Stage 1 high BP is specified as systolic BP between 140 and 160. What percentage of adults in the US qualify for stage 1? 12. Use the Stats_2 sheet to answer this question. a. Use the COUNTIFS function to get the percentage of values in "Category" (column C) that say "Rush" b. Use the percentage from part a to get the probability that from a random sample of 100 Category values, that between 30 and 35 would be Rush. )? j. Make a histogram with 10 groups for Profit (column J) and copy and paste it below. K. Is your data for Profit Normal, Skewed left or Skewed right? 13. Use column I (Total) of the Excel sheet Stats_2 to answer the following questions. a. Make a histogram of the data in column I (total) with 10 groups. Title your graph and title the horizontal and vertical axis and copy and paste your histogram below. b. What is the mean and median of all the data in column I. c. Using parts a and b do you believe the data is approximately normally distributed? Why? d. Get the population standard deviation for the data in column I. e. Use the mean and standard deviation that you calculated in parts b and d to get a z-score for a Total of $1518.03. f. Use the z-score from part e to get the percentage of Total values that are less than $1518.03 g. Use the COUNTIFS function to get the number of Total values in column I that are less than $1518.03 h. Get the percentage of Totals that are less than $1518.03. i. How close is your answer to part f (using z-scores) to your answer to part h (the actual percentage)? j. Make a histogram with 10 groups for Profit (column J) and copy and paste it below. K. Is your data for Profit Normal, Skewed left or Skewed right