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Suppose you were to flip a fair coin 12 times and you recorded the number of “Tails” that you received. Find the probability that you would get anywhere from 3 to 8 “Tails”. Make sure to type in your answer rounded to 2 decimal places. For example, if you thought the answer was 1.23456, then you would type in 1.23.

Suppose you roll a standard 6-sided die one time. What is the probability that you would roll a number less than 4? Recall that the sample space for this scenario would be .   Make sure to type in your answer as a decimal rounded to 2 decimal places. For example, if you thought the answer was 0.12345 then you would type in 0.12. 

Suppose you were to flip a fair coin 9 times and you recorded the number of “Tails” that you received. Find the probability that you would get exactly 5 “Tails” out of 9 coin tosses.  Make sure to type in your answer rounded to 2 decimal places. For example, if you thought the answer was 1.23456, then you would type in 1.23.

A professor was interested in comparing how well her students performed on their midterm and final exams in her calculus course. She randomly sampled 7 students from her class and recorded their midterm and final exam grades which are shown in the table below.  Midterm and Final Exam Grade Comparisons Student X=Midterm Exam Y=Final Exam Student 1 59 76 Student 2 65 67 Student 3 92 93 Student 4 80 92 Student 5 56 66 Student 6 50 68 Student 7 67 88   Use this information to calculate Pearson’s correlation coefficient.  Make sure to type your answer as a decimal rounded to 3 decimal places. For example, if you thought the answer was 0.54321 then you would type in 0.543.  

Suppose you were trying to determine if there was a difference in the means of 4 different groups, and instead of using an ANOVA test, you decided to carry out 6 separate 2-sample t-tests to compare every possible combination of groups and you set the Type I error rate as 

Suppose you have a jar that contains 100 marbles: 35 red, 15 blue, 20 green, and 30 black. If you were to select 1 marble at random from the jar, what is the probability that you would select either a red or black marble?   Type in your answer as a decimal rounded to 2 places. For example, if you thought the answer was 54.321% then you would type in 0.54. 

A professor was interested in comparing how well her students performed on their midterm and final exams in her calculus course. She randomly sampled 7 students from her class and recorded their midterm and final exam grades which are shown in the table below.  Midterm and Final Exam Grade Comparisons Student X=Midterm Exam Y=Final Exam Student 1 75 76 Student 2 73 67 Student 3 87 93 Student 4 90 92 Student 5 72 66 Student 6 84 68 Student 7 91 88   Use this information to calculate Pearson’s correlation coefficient.  Make sure to type your answer as a decimal rounded to 3 decimal places. For example, if you thought the answer was 0.54321 then you would type in 0.543.  

Consider the table below that shows how many students from each year are in each of the Hogwart’s houses. Use this information to answer the probability question that follows.  Hint: I would recommend finding the totals for each row and column first.  Probability Table Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Ravenclaw 30 38 34 33 39 31 35 Hufflepuff 36 33 29 37 39 35 34 Gryffindor 32 36 41 32 33 35 35 Slytherin 34 32 36 39 33 32 31   Find the probability that a randomly selected student is in year 4 and from Gryffindor.    Make sure to type in your answer as a decimal rounded to 3 decimal places. For example, if you thought the answer was , then you would type in 0.431.

A study was conducted to determine voter’s political party preferences in various cities in Kern County. The researchers conducting the study randomly sampled 100 individuals from these cities In the table below you can see the breakdown of how these individuals responded based on the city that they live in. Political Party Preference by City Republican Democrat Other No Preference Bakersfield 43 34 9 14 Taft 50 21 10 19 Arvin 11 65 10 14   Use this information to carry out an appropriate test at the

A professor was interested in comparing how well her students performed on their midterm and final exams in her calculus course. She randomly sampled 7 students from her class and recorded their midterm and final exam grades which are shown in the table below.  Midterm and Final Exam Grade Comparisons Student X=Midterm Exam Y=Final Exam Student 1 59 86 Student 2 65 77 Student 3 92 70 Student 4 80 92 Student 5 56 95 Student 6 50 93 Student 7 67 89   Use this information to calculate the y-intercept of the least squares regression line.  Make sure to type your answer as a decimal rounded to 3 decimal places. For example, if you thought the answer was 98.76543 then you would type in 98.765.