1 5) Since the die is fair, on average, approximately- of the rolls should be 4's. So when the die is rolled 600 times approximately 100 of the tosses should be 4's. What is the actual number of 4's for 600 rolls as given by the chart? e) What is the difference between the number of 4's we should expect on average, 100, and the actual number of 4's For 600 rolls? ) What is the difference between the percent we expect to be 4's on average, 16.67 %, and the relative frequency as a percent from the table for 600 rolls? %

4. The English teacher at your school wants to randomly select students to present a scene from a Shakespeare play in class. There are four roles to fill, two for males and two for females. Describe a process that would use random numbers to select the people to contact. There are 9 males and 11 girls in this class.

5. Let's estimate using simulation. To do that, simulate the event of tossing a dart into a unit square in Excel and count how many darts fall into an inscribed circle of the unit square. (Hint: Use =Rand() to generate a number from Uniform(0,1) in Excel.) Then compute an estimate of 7 using the ratio of the darts that had fallen into the circle based on 50, 100, 500, 1000, 3000, 5000 tosses, respectively. Also answer the following questions. (a) Does the estimate seem to converge to the true value of 7 as the number of tosses increase? Why? (b) Compute the 95% confidence intervals of these estimates. Explain in words the meaning of the confidence interval.

A researcher wishes to estimate the proportion of households with two cars.a) How large a sample is needed in order to be 99% confident that the sample proportion will not differ from the true proportion by more than 3%?b) Repear part a if a previous study indicates that the proportion of households with two cars is 25%.

g) The Lady Tasting Tea Experiment. An English lady, Muriel Bristol, claimed that she can tell whether tea or milk was added first to a cup. So as a researcher, you want to test whether she can really tell whether tea or milk was added first. But how would you do it? A possible research design: Give her eight cups, four where tea is added first and the other four where milk is added first, in random order. Then ask her to pick out the four cups where the milk is added first. After you conducted the experiment and collected the data, how do you decide whether she can truly tell the difference or she was just guessing. Our intuition tells us that the more cups she gets correctly, the more likely that she is NOT guessing. "If the Lady is just guessing, the probability of getting it all correctly is 1.4%." Now using your knowledge on combinatorics and probability, explain how this number was calculated? h) Suppose you flip four fair coins. What is the probability that you will get all…

Suppose we want to estimate the proportion of the Helena population who have used marijuana within the last month. We select 4328 participants and ask them each to first privately draw a card from a standard 52-card deck. If they get a “club” they are asked to respond truthfully to the question “Have you used marijuana within the last month?”If they get any other suit they are asked to respond to the question “Does your phone number end in an odd digit?”The study is blinded in the sense that the researcher doesn’t know which question the participant is answering. Hence, participants are guaranteed anonymity and are more likely to be truthful in their responses. The researchers only get a “yes” or “no” answer from each respondent and don’t know the actual results of the card draw. What is the expected probability of a person’s phone number ending in an odd digit? What is the expected probability of a person’s phone number not ending in an odd digit?

11) What is the percentage of players whose height is less than 70 inches? (pAes) 12) What is the percentage of players whose height is between 64 inches and 68 inches? mguto

a) Suppose the mean (average) of the 10 numbers is 35, median is 31. If you change only the 9th number, do you think both mean and median will change? b) If you add 13 to the 11th number what is the new mean? what is the new median?

A​ stem-and-leaf plot for the number of touchdowns scored by all Division 1A football teams is shown below. Complete parts​ (a) through​ (c). a) If a team is selected at​ random, find the probability the team scored at least 30 touchdowns. b)if a steam is selected at random,find the probability the team scored between 40 and 48 touchdowns inclusive . c)if a team is selected at random,find the probability the team scored more than 78 touchdowns. are. Any of these events unusual? 1 3 4 5 7 8 8 ​ Key:1|5equals=15 2 0 1 2 2 3 4 5 7 8 8 9 3 0 0 1 1 1 2 2 3 3 4 4 5 5 7 7 7 8 9 4 0 0 1 2 2 3 4 5 5 5 5 6 7 8 8 9 5 0 2 3 5 5 7 8 6 1 3 6 7 7   8 7

The mean age and median age of 5 people in a room is 40 years. A person whose age is 20 years leaves the room. a) If possible, determine the mean age of the remaining 4 people in the room. If it is not possible to find the mean age of the remaining 4 people, write "not possible" (without the quotes) as your answer.  b) If possible, determine the median age of the remaining 4 people in the room. If it is not possible to find the median age of the remaining 4 people, write "not possible" (without the quotes) as your answer.