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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 between 110 and 122?   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 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 4 B 5 C 14 D 4 F 1 What percentage of students passed the class with a ‘C’ or better? (Cumulative Relative Frequency) Give your answer as a percentage rounded to 2 decimal places (i.e. If the answer is 17.43%, simply type in 17.43)

Suppose a local pizzeria delivers pizzas every day of the week and their delivery times are normally distributed with a mean of 30 minutes with a standard deviation of 4 minutes. Determine the interval that contains the middle 60% of delivery times. Explain how you arrived at your answer.    Hint: Try sketching the normal distribution defined above and using percentiles, and shade the desired region Make sure to type your interval in an interval format with your bounds rounded to 2 decimal places. For example, if you thought the lower bound was 50.123 and the upper bound was 60.123 then you would type (50.12, 60.12) as your interval. 

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 of at most 106?   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 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 96 and greater than 103?   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 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 131?   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 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 of more than 124?   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.

The CBEST is a test that individuals in California must take before they can become substitute teachers at the K-12 level. One portion of the exam is devoted to mathematics and it consists of 50 multiple choice questions that each have 5 possible options. Suppose Jim took the CBEST test and decided to randomly guess on all 50 questions. Use this information to answer the following question.  What is the probability that Jim gets anywhere from 8 to 17 correct? Make sure to type in your answer as a decimal rounded to 3 decimal places. For example, if you thought the answer was 0.54321 then you would type in 0.543.

Consider a town where the average age of all individuals is 34.2 years old with a standard deviation of 18.5 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 35 years old or greater than 28 years old?

Consider a town where the average age of all individuals is 36.6 years old with a standard deviation of 17.3 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 28 years old and greater than 41 years old?