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A study was conducted of college students that stated the true average number of units that a college student enrolls in each semester is 12.7 with a true standard deviation of 6.8. Suppose you randomly sampled 40 college students and recorded the number of units that each of them were enrolled in. Use this information to answer the following question.  What is the probability that the average number of units those students from your sample were enrolled in was less than 12.8.? Make sure to round your answer to 2 decimal places; i.e. if your answer was 0.54321 then you would type in 0.54. 

Isabella works for an insurance company and she is the director of the customer service department. One of her main goals is to reduce the wait times that customers experience when they call the department before they are connected to someone that can help them. She recorded all of the wait times that customers experienced in a given month and recorded it in the frequency distribution table below.  Suppose you were to construct a histogram based on this data (starting with the 0-5 minute group on the far left) identify what the overall shape of the data would look like.  Customer Wait Time Breakdown Minutes Spent Waiting Frequency 0 – 5 109 6-10 63 11-15 41 16-20 13 21-25 10 26+ 4  

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 0.11 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. 

A study was conducted in 2018 to look at average annual salaries for individuals who lived in Wisconsin. It found that on average individuals in Wisconsin earned $56,302 per year. Assume the true standard deviation for annual salary was $8,000. Suppose you took a random sample of 50 individuals from Wisconsin in 2018 and recorded their salaries. Use this information to answer the following question. What is the probability that the average salary for those 50 individuals in your sample would fall between $49,000 and $57,000 per year? Make sure to round your answer to 2 decimal places; i.e. if your answer was 0.54321 then you would type in 0.54. 

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 1.23 hours per day on their tablets. Assume the true standard deviation amount of time that someone spends on their tablet per day is 2.57 hours. Use this information to construct and interpret an 88% 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. 

Consider a town where the average age of all individuals is 34.3 years old with a standard deviation of 14.7 years. Suppose you were to randomly select 50 individuals from this town as part of a study.  What is the probability that the average age of the 50 individuals in your study would be less than 40 years old and greater than 50 years old?

A study was conducted that found 15% of all US adults have some form of student loan debt. Suppose you were to randomly sample 100 US adults. What is the probability that at anywhere from 20 to 25 of them would have student loan debt? Use a binomial distribution to answer this question. Make sure to round your answer to 2 decimal places; i.e. if your answer was 0.654321 then you would type 0.65

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.