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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 92 or greater than 113?   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.

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 16 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 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 28 students in his class and their final letter grades are shown below.  Distribution Table of Letter Grades Letter Grade Count/Frequency A 6 B 6 C 11 D Left Blank on Purpose F 1 Total 28 What percentage (relative frequency) of students received a D? Give your answer as a percentage rounded to 2 decimal places (i.e. If the answer is 17.43%, simply type in 17.43)

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 $300 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. 

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 33 students in his class and their final letter grades are shown below.  Distribution Table of Letter Grades Letter Grade Count/Frequency A 6 B 9 C 11 D Left Blank on Purpose F 3 Total 33 What percentage (relative frequency) of students received a D? Give your answer as a percentage rounded to 2 decimal places (i.e. If the answer is 17.43%, simply type in 17.43)

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 71 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 construct a 90% confidence interval for the true population mean GPA of students at Taft College. If you increased the sample size and left all of the other sample values constant, then what would happen to the width of the confidence interval?

Suppose you are hired to determine the true average amount of money that college students make while working on-campus jobs. If you want to be 95% confident that you are within $100 of the actual value, how many students would you need to survey? Assume that the true standard deviation is $600.  Reminder: It’s impossible to survey a fraction of a college student.  

A business professor was interested in seeing how students had fared on her final exam over the years. She looked back at students who had taken her class over the last 5 years and recorded their exam scores and summarized that information in the table below. Suppose you were to construct a histogram based on this data (starting with 0-9 group on the far left) identify what the overall shape of the data would look like.  Final Exam Breakdown Final Exam Score Frequency 0 – 9 0 10 – 19 1 20 – 29 1 30 – 39 0 40 – 49 3 50 – 59 4 60 – 69 9 70 – 79 38 80 – 89 56 90 – 100 48

Suppose you are hired to determine the true average amount of money that college students make while working on-campus jobs. If you want to be 95% confident that you are within $90 of the actual value, how many students would you need to survey? Assume that the true standard deviation is $600.  Reminder: It’s impossible to survey a fraction of a college student.