Part 2: The graph below represents the relative frequency of 4's that occur (number of 4's divided by the total numberof rolls) versus the number of times the die was rolled for the first 1000 rolls. The table shows these values, and inaddition, the total number of 4's for the 591st to 600th rolls. Use this information to answer the questions below.Long Term Relative Frequency10.90.80.70.60.50.40.30.20.1100 200 300 400 500 600 700 800 900 1000Number of Die RollsLong Term Relative FrequencyNumber ofRolls591592593594595596597598599600Number of 4's101101102102102102102102102102RelativeFrequencyof 4's0.1709 0.1706 0.172 0.1717 0.1714 0.17110.1709 0.1706 0.1703 0.17d) Since the die is fair, on average, approximately - of the rolls should be 4's. So when the die is rolled 600 timesapproximately 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'sfor 600 rolls?f) What is the difference between the percent we expect to be 4's on average, 16.67 % , and the relative frequency asa percent from the table for 600 rolls?%Relative Frequency of 4

d) Actual Number of 4 rolls given in the chart is 102

Answered: 1 5) Since the die is fair, on average,…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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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.
33- In a group of 100 students from the engineering faculty, the attendance status (Continue / Discontinue) and the 3 departments they studied It is desired to investigate whether there is a relationship between (Industry / Computer / Machinery) departments. The measurement format of the variable to be compared why? a) All available B) Sortable qualitative data NS) Classifiable qualitative data D) Proportional qualitative data TO) Measurable qualitative data
The mean score in statistics of 50 students in a class was 72 and that of the 15 girls was 65. Find the mean score of the boys in the class. a) 74 b) 75 c) 73 d) 76
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?
3. Pick any number, multiply the number by 5, and add 10 to the number. Divide the sum by 5. Subtract 1 from the quotient. a) What is the relationship between the number you started with and the final answer? (might need to choose random numbers and apply procedure multiple times before noticing pattern) Ingresb sd3 ni (saie yns to) assup2 to 19dmin odd saianstad T b) Prove, using deductive reasoning (algebra), the conjecture made in part (a). Needs to be a general proof not a particular numerical example.
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

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