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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.

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 1.20 hours per day on their tablets. Assume the true standard deviation amount of time that someone spends on their tablet per day is 2.66 hours. Use this information to construct and interpret a 93% 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 35.6 years old with a standard deviation of 13.7 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 30 years old and greater than 40 years old?

A study was conducted that found 46.9% of all smartphone users in the US had an iPhone. Suppose you were to randomly sample 40 US smartphone users. What is the probability that at least 18 of them had an iPhone? 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

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 23 to 40 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