Blog

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?

In 2018, a study was conducted that stated that the average commute time to work for Kern County residents was 22.6 minutes. Suppose you were hired to determine if the average commute time is different than it was in 2018. You randomly sample 87 individuals who commute to work from Kern county and you find that their average commute time was 20.8 minutes and you find the sample standard deviation of commute times for those 87 individuals was 3.6 minutes.  Carry out the appropriate hypothesis test at the

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 120 or greater than 102?   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 93 and greater than 108?   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 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 less than 12.2.? Make sure to round your answer to 2 decimal places; i.e. if your answer was 0.54321 then you would type in 0.54. 

In 2018, a study was conducted that stated 22.6% of residents in Kern County live below the poverty line. Suppose you were hired to determine if that percentage has changed since the study was conducted. You randomly sample 200 residents from Kern County and find that 35 of them fall below the poverty line. Carry out the appropriate hypothesis test at the

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 1 10 – 19 1 20 – 29 3 30 – 39 4 40 – 49 5 50 – 59 5 60 – 69 12 70 – 79 25 80 – 89 34 90 – 100 44

Consider the following distribution of letter grades shown below for a calculus class. Create a bar graph of the data (making sure to order the data properly) and identify the shape of the distribution. Distribution Table of Letter Grades Letter Grade Count/Frequency A 8 B 8 C 8 D 8 F 8