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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 at least 19 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 professor at CSUB, was trying to determine whether freshmen or seniors at CSUB were more likely to attend CSUB’s home basketball games. He randomly sampled 12 freshmen and 4 seniors from the Men’s Track & Field team and asked them whether or not they had been to a basketball game at CSUB. Out of the 4 seniors, 3 said they had been to a home basketball game. Out of the 12 freshmen, 4 said they had been to a home basketball game. Based on the situation described above, state whether the professor conducted an observational or an experimental study. Justify your answer. 

In your own words, what is the difference between a discrete random variable and a continuous random variable?

A survey was taken of students enrolled in STEM classes at Taft College. One of the questions asked which city the students live in, and one of the other questions asked about their major. The results are shown below. Use them to answer the probability question that follows.  Probability Table Bakersfield Taft Shafter Other Math 3 5 2 4 Chemistry 9 4 1 5 Biology 4 13 8 6 Engineering  14 15 2 1 Physics 3 1 0 2   What is the probability that a randomly selected student from this survey lives in Shafter?    Make sure to type in your answer as a decimal rounded to 3 decimal places. For example, if you thought the answer was 0.12345 then you would type in 0.123. 

A survey was taken of students enrolled in STEM classes at Taft College. One of the questions asked which city the students live in, and one of the other questions asked about their major. The results are shown below. Use them to answer the probability question that follows.  Probability Table Bakersfield Taft Shafter Other Math 3 5 2 4 Chemistry 9 4 1 5 Biology 4 13 8 6 Engineering  14 15 2 1 Physics 3 1 0 2   What is the probability that a randomly selected student from this survey is a math major given that they live in Shafter?   Make sure to type in your answer as a decimal rounded to 3 decimal places. For example, if you thought the answer was 0.12345 then you would type in 0.123. 

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 at least 10 questions 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.

Scenario: A math professor is interested in determining the true proportion of all students at his school that prefer online math classes as opposed to in-person math classes. However, the professor didn’t have enough time to survey every student at the school. Therefore, the professor decided to survey students from each of his classes. He randomly selected 12 students from each of his 4 classes and asked them whether they would prefer to take their math classes online or in-person. 32 out of the 48 students stated that they would prefer in-person classes while 16 of the 48 stated they would prefer to take them online.    Consider the scenario above and answer the following questions: What is the population of interest? What is the parameter of interest? What is the sample statistic?

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 130 students who were taking math classes that semester, and 35 of them stated that they preferred taking their math classes online while 95 of them preferred taking them face to face. Construct and interpret a 96% 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

A survey was taken of students enrolled in STEM classes at Taft College. One of the questions asked which city the students live in, and one of the other questions asked about their major. The results are shown below. Use them to answer the probability question that follows.  Probability Table Bakersfield Taft Shafter Other Math 3 5 2 4 Chemistry 9 4 1 5 Biology 4 13 8 6 Engineering  14 15 2 1 Physics 3 1 0 2   What is the probability that a randomly selected student from this survey is not an engineering major?   Make sure to type in your answer as a decimal rounded to 3 decimal places. For example, if you thought the answer was 0.12345 then you would type in 0.123. 

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 at most $61,850? 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.