A study was conducted on the fuel economy of vehicles in the U.S. The study found that cars that ran on gasoline averaged 24.2 MPG. Assume this data is normally distributed with a standard deviation of 3.7 MPG. Use this information to answer the following question.    What MPG would correspond to the 90th percentile of all cars in the US that run on gasoline?  Make sure to round your answer to 2 decimal places. For example, if your answer was 87.654321 then you would type in 87.65. 

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? Make sure to round your answer to 2 decimal places. For example, if your answer was 0.654321 then you would type 0.65

A study was conducted to determine how movie lengths vary based on genre. As a part of that larger study, it was found that the average length of all movies is 117 minutes. Assume this data is normally distributed with a standard deviation of 26 minutes. Use this information to answer the following question.    What is the probability that a randomly selected movie is either shorter than 105 minutes or longer than 130 minutes?  Make sure to round your answer to 2 decimal places (For example, if your answer was 0.654321 then you would type 0.65)

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 more than 13.1?  Make sure to round your answer to 2 decimal places. For example, if your answer was 0.654321 then you would type 0.65

Doogan is taking Statistics and has just learned about confidence intervals. He makes the following statement: “If all other sample values are held constant, then increasing the confidence level from 90% to a higher percentage will always result in a wider confidence interval, regardless if you are dealing with means or proportions.” Do you agree/disagree with his statement? If you agree, then write a few sentences justifying why this statement is true. If you disagree, then provide a counterexample where this property doesn’t hold and specify which sample values you utilized. 

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 500 teenagers and they found that 184 of them were planning on purchasing the game when it comes out.   Use this information to construct and interpret a 94% 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. 

Consider a town where the average age of all individuals is 34.5 years old with a standard deviation of 12.2 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 38 years old or greater than 36 years old? Make sure to round your answer to 2 decimal places. For example, if your answer was 0.654321 then you would type 0.65

A local restaurant was trying to figure out the best way to advertise to attract new customers from this town. The owner had a set amount of money to spend on advertising and they were trying to figure out if it was better to invest in advertisements on social media or television commercials. They conducted a survey of 500 local residents to gauge if they spent more time on social media or watching television. Out of the 500 residents who were surveyed, 222 of them stated that they spent more time on social media than watching television.    Use this information to carry out the appropriate hypothesis test at the

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 28 times and recorded how long it took each time to make an informed decision. On her 28 trips using route A, she took an average of 40 minutes with a standard deviation of 5.4 minutes. On her 28 trips using route B, she took an average of 40 minutes with a standard deviation of 5.9 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 (For example, if your answer was 0.654321 then you would type 0.65)