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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 95 or greater than 121?   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 math professor was interested in figuring out whether students taking mathematics classes  at his school preferred to take them online or face to face. He decided to randomly survey students taking mathematics classes that semester. He ended up surveying 120 students who were taking math classes that semester, and 37 of them stated that they preferred taking their math classes online while 83 of them preferred taking them face to face. Construct and interpret a 95% confidence interval for the true proportion of students at the school that prefer to take math classes face to face.  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 are working on a political campaign. You are tasked to figure out what proportion of voters are in favor of your candidate. You want to be 95% confident within 3% of the true proportion. What sample size would be required in this scenario?

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 89?   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 no more than 14 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.

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 98 or greater than 110?   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.

IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. Use this information to answer the following question. What is the probability that a randomly selected person will have an IQ score anywhere from 90 to 103? 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.

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 value below.  What IQ score would represent the 63rd percentile?   Make sure to write your answer as a decimal rounded to 3 decimal places. For example, if you thought the answer was 123.4567 then you would type in 123.457.

A study was conducted and it found that the mean annual salary for all California residents was $63,783 and the true standard deviation for all California residents was $7,240. Suppose you were to randomly sample 50 California residents. Use this information to answer the following question.  What is the probability that the average salary for the 50 individuals in your sample would be anywhere from $64,000 to $67,000? 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.

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 value below.  What IQ score would represent the 83rd percentile?   Make sure to write your answer as a decimal rounded to 3 decimal places. For example, if you thought the answer was 123.4567 then you would type in 123.457.