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Suppose you were to flip a fair coin 7 times and you recorded the number of “Tails” that you received. Find the probability that you would get exactly 6 “Tails” out of 7 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 study was conducted at a local community college was conducted to determine whether or not students were in favor of having a 1-week break in the fall semester over the Thanksgiving break. In order to accommodate the week long break, the fall semester would have to start 1 week earlier in the summer, and so the decision makers at the college wanted student’s opinions to see if they were in favor of the change. Out of the 110 students that were included in the survey, 93 stated that they were in favor of the week long break in the fall while 17 students were against that change.  Construct and interpret a 94% confidence interval for the true proportion of students at the school that are in favor of the change.   Make sure to address the following in your response: Check any and all relevant assumptions and state how you determined whether or not they were satisfied (Be as specific as possible) Make sure to type your confidence interval in an interval format with each bound rounded to 3 decimal places [i.e. (12.345, 45.678)] Make sure to include an interpretation in context of the given problem  

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 8 to 10 “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.

A study was carried out by a gaming company to try and determine the true proportion of teenagers that were interested in an upcoming video game they were releasing. The company decided to randomly survey 300 teenagers and they found that 88 of them were planning on purchasing the game when it comes out. Use this information to construct and interpret a 98% confidence interval for the true proportion of teenagers who plan to purchase the video game when it comes out. Make sure that you are addressing the following in your response.  Check any and all relevant assumptions and state specifically how they are/aren’t satisfied State the desired confidence interval (round any values in your interval to 2 decimal places, i.e. 54.321 would be rounded to 54.32) Interpret the interval in context of the scenario provided. 

The owner of a local restaurant was interested in figuring out the true proportion of their customers that eat at their restaurant on a monthly basis. They knew that they wanted to be accurate within 0.03 of the true actual proportion with 95% confidence. In order to meet these requirements, how large of a sample should they take? Make sure to round your answer properly since it is impossible to survey a fraction of an individual. 

The CEO of a major tech company was interested in developing a new type of tablet. However, before she decided how much money she wanted to invest in research and development, she wanted to conduct a survey to determine the average amount of time a person spends on their tablet each day. She had her employees conduct a survey of 1000 randomly selected individuals who owned tablets. As part of the survey, they found that those 1000 individuals spent an average of 1.45 hours per day on their tablets. Assume the true standard deviation amount of time that someone spends on their tablet per day is 2.88 hours. Use this information to construct and interpret an 85% confidence interval for the true average amount of time a person spends on their tablet each day.  Make sure that you are addressing the following in your response.  Check any and all relevant assumptions and state specifically how they are/aren’t satisfied State the desired confidence interval (round any values in your interval to 2 decimal places, i.e. 54.321 would be rounded to 54.32) Interpret the interval in context of the scenario provided. 

According to the Bureau of Labor Statistics, in 2019 U.S. households spent an average of $386.92 per month on food. Assume this data is normally distributed with a standard deviation of $112. Use this information to answer the following question.  What Z-score would correspond to a household that spent an average of $450 on food per month in 2019? Make sure to round your answer to 2 decimal places; i.e. if your answer was 87.654321 then you would type in 87.65. 

Eliza had a long commute to work each day and she was always worried about running late. When it came to distance, both drives were the same number of miles from her home, but one of them had a few more stoplights on her way. She wanted to find the most consistent route so she could know exactly how long it would take her to go to work each day. She decided to travel each route 25 times and recorded how long it took each time to make an informed decision. On her 25 trips using route A, she took an average of 40 minutes with a standard deviation of 3.1 minutes. On her 25 trips using route B, she took an average of 40 minutes with a standard deviation of 4.6 minutes. Assume the commute times using both routes are normally distributed.  Use this information to carry out the appropriate hypothesis test at the

The average height for an NCAA Division 1 men’s basketball player is 77 inches. Assume this data is normally distributed with a standard deviation of 8 inches. Use this information to answer the following question.  What is the probability that a randomly selected NCAA D1 men’s basketball player is at least 78.5 inches tall? Make sure to round your answer to 2 decimal places; i.e. if your answer was 0.654321 then you would type in 0.65. 

Suppose you roll a standard 6-sided die and you recorded the number of times that you ended up rolling an even number. Find the probability that you would get no less than 1 even number out of 5 rolls of the dice. 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.