Some believe that Captain America can run the fastest mile of any person alive. In order to test this theory, Captain America decided to run the mile multiple times and record how long it took him (in seconds) to run each one. He decided to attempt running the mile 40 times and determine his average mile time. Let’s assume his true mean mile time was 138 seconds with a standard deviation of 16 seconds. Use this information to find the following probability.  What is the probability that his average mile time would be greater than 137 seconds?   Make sure to round your final answer to 3 decimal places. For example, if you thought the answer was 0.123456 then you would type in 0.123.

ANA: Hablo del [q1] y [q2].

A professor at a local community college decided to try out a new lecture format for his statistics class, and he was curious how well students performed using this new format. So the professor decided to record every student’s final grade at the end of the semester to determine how effective this new lecture format was. There were 26 students in his class and their final letter grades are shown below.  Distribution Table of Letter Grades Letter Grade Count/Frequency A 4 B 8 C Left Blank on Purpose D 3 F 1 Total 26 What percentage (relative frequency) of students received a C? Give your answer as a percentage rounded to 2 decimal places (i.e. If the answer is 17.43%, simply type in 17.43)

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 6 “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 potato chip manufacturer was building a new manufacturing plant, and they were trying to decide whether or not they wanted to change the equipment/machine they were currently using to bag the potato chips. They had noticed a wide variability in the weight of the potato chip bags that were being produced with their current equipment, and they wanted to reduce the variability. Therefore, they decided to determine if a newer machine would help them reduce the variability in the weights of the bags. They randomly sampled the weights of 50 bags from their current machine and 50 bags from the new machine and both of them recorded an average weight of 10 ounces. However, the current machine had a standard deviation of 0.16 ounces and the new machine had a standard deviation of 0.09 ounces. Carry out the appropriate hypothesis test at the

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 roll a standard 6-sided die one time. What is the probability that you would roll an odd number? 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. 

A recent study was conducted and it found that IQ’s are normally distributed with a mean of 100 and a standard deviation of 15. Use this information to find the following probability.  What is the probability that a randomly selected individual would have an IQ less than 98 or greater than 110?   Make sure to write your answer as a decimal rounded to 3 decimal places. For example, if you thought the answer was 23.173% then you would type in 0.232.

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 from Year 3.    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.

Daniel was playing a board game with his family and he felt as if the die that they were using was an unfair die because it appeared as if some numbers were occurring more frequently than others, and he didn’t believe this was just due to random chance. Therefore, at the end of the game night, Daniel decided to roll the die 60 times and record the number of times that each number appeared. Those results are shown in the table below.  Dice Counts Number on Die 1 2 3 4 5 6 Count 8 14 8 8 14 8   Use this information to carry out an appropriate test at the